<p>Dois bêbados começam a caminhar sobre uma linha reta, a partir da origem, dando passos de mesmo comprimento para a direita ou para a esquerda, com a mesma probabilidade. Suponha que os passos dos dois sejam simultâneos. Ache a probabilidade de que eles se encontrem novamente depois de dar <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.064ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 888.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title” data-mathml="undefined">
<title> N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”/>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”/>
</g>
</svg> passos.</p>
<title> N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”/>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”/>
</g>
</svg> passos.</p>
Passo 1
<p>Olá! Bora pra mais uma?</p>
<p>Dois bêbados começam na origem e dão, simultaneamente, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.064ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 888.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
</g>
</svg> passos de mesmo comprimento para direita ou esquerda com probabilidade <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.487ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 1501.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 1 / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMAIN-31" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“500” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1001” y=“0”></use>
</g>
</svg> cada, independentemente um do outro. Queremos a probabilidade de que, após <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.064ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 888.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
</g>
</svg> passos, eles <b>se encontrem</b> novamente (ou seja, estejam na mesma posição).</p>
<p><b>Como vamos resolver isso?</b></p>
<p>Vamos modelar:Seja <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.143ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1353.1 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X n </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6E” d=“M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6E" x=“1171” y="-213"></use>
</g>
</svg> = posição do bêbado 1 após <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.395ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 600.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> n</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6E” d=“M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6E" x=“0” y=“0”></use>
</g>
</svg> passos (passo = ±1).Seja <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.569ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1106.1 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Y n </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6E” d=“M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6E" x=“822” y="-213"></use>
</g>
</svg> = posição do bêbado 2 após <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.395ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 600.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> n</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6E” d=“M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6E" x=“0” y=“0”></use>
</g>
</svg> passos.Ambos começam em 0: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“12.743ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 5486.4 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X 0 = Y 0 = 0</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-30" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1560” y=“0”></use>
<g transform=“translate(2616,0)”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-30" x=“822” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“3929” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“4985” y=“0”></use>
</g>
</svg>.</p>
<p>Os incrementos são independentes entre si e entre os dois bêbados.Eles se encontram após <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.064ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 888.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
</g>
</svg> passos se <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“9.756ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 4200.6 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X N = Y N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<g transform=“translate(2890,0)”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“822” y="-213"></use>
</g>
</g>
</svg>.</p>
<p>Defina <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“16.212ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 6980.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> D N = X N - Y N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-44” d=“M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-44" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<g transform=“translate(2890,0)”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-2212" x=“4669” y=“0”></use>
<g transform=“translate(5670,0)”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“822” y="-213"></use>
</g>
</g>
</svg>. Eles se encontram se <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.877ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3391.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> D N = 0</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-44” d=“M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-44" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“2890” y=“0”></use>
</g>
</svg>.</p>
<p>Note que <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“14.485ex” height=“3.509ex” style=“vertical-align: -1.005ex;” viewBox=“0 -1078.4 6236.5 1510.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X N = ∑ i = 1 N a i </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJSZ1-2211” d=“M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<g transform=“translate(2890,0)”>
<use xlink:href="#E1-MJSZ1-2211" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1494” y=“675”></use>
<g transform=“translate(1056,-287)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-3D" x=“345” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1124” y=“0”></use>
</g>
<g transform=“translate(2471,0)”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
</g>
</g>
</g>
</svg>, onde <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“8.099ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3486.9 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = ± 1</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-B1” d=“M56 320T56 333T70 353H369V502Q369 651 371 655Q376 666 388 666Q402 666 405 654T409 596V500V353H707Q722 345 722 333Q722 320 707 313H409V40H707Q722 32 722 20T707 0H70Q56 7 56 20T70 40H369V313H70Q56 320 56 333Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1151” y=“0”></use>
<use xlink:href="#E1-MJMAIN-B1" x=“2207” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2986” y=“0”></use>
</g>
</svg> com probabilidade 1/2.Analogamente, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“13.679ex” height=“3.509ex” style=“vertical-align: -1.005ex;” viewBox=“0 -1078.4 5889.5 1510.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Y N = ∑ i = 1 N b i </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJSZ1-2211” d=“M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“822” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1587” y=“0”></use>
<g transform=“translate(2643,0)”>
<use xlink:href="#E1-MJSZ1-2211" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1494” y=“675”></use>
<g transform=“translate(1056,-287)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-3D" x=“345” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1124” y=“0”></use>
</g>
<g transform=“translate(2471,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
</g>
</g>
</svg>, com <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.866ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3386.9 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> b i = ± 1</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-B1” d=“M56 320T56 333T70 353H369V502Q369 651 371 655Q376 666 388 666Q402 666 405 654T409 596V500V353H707Q722 345 722 333Q722 320 707 313H409V40H707Q722 32 722 20T707 0H70Q56 7 56 20T70 40H369V313H70Q56 320 56 333Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1051” y=“0”></use>
<use xlink:href="#E1-MJMAIN-B1" x=“2107” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2886” y=“0”></use>
</g>
</svg> com probabilidade 1/2.</p>
<p>Então:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“21.064ex” height=“7.509ex” style=“vertical-align: -3.171ex;” viewBox=“0 -1867.7 9069.4 3233.2” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> D N = ∑ i = 1 N ( a i - b i ) .</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-44” d=“M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJSZ2-2211” d=“M60 948Q63 950 665 950H1267L1325 815Q1384 677 1388 669H1348L1341 683Q1320 724 1285 761Q1235 809 1174 838T1033 881T882 898T699 902H574H543H251L259 891Q722 258 724 252Q725 250 724 246Q721 243 460 -56L196 -356Q196 -357 407 -357Q459 -357 548 -357T676 -358Q812 -358 896 -353T1063 -332T1204 -283T1307 -196Q1328 -170 1348 -124H1388Q1388 -125 1381 -145T1356 -210T1325 -294L1267 -449L666 -450Q64 -450 61 -448Q55 -446 55 -439Q55 -437 57 -433L590 177Q590 178 557 222T452 366T322 544L56 909L55 924Q55 945 60 948Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJSZ4-28” d=“M758 -1237T758 -1240T752 -1249H736Q718 -1249 717 -1248Q711 -1245 672 -1199Q237 -706 237 251T672 1700Q697 1730 716 1749Q718 1750 735 1750H752Q758 1744 758 1741Q758 1737 740 1713T689 1644T619 1537T540 1380T463 1176Q348 802 348 251Q348 -242 441 -599T744 -1218Q758 -1237 758 -1240Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2E” d=“M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z”></path>
<path stroke-width=“1” id=“E1-MJSZ4-29” d=“M33 1741Q33 1750 51 1750H60H65Q73 1750 81 1743T119 1700Q554 1207 554 251Q554 -707 119 -1199Q76 -1250 66 -1250Q65 -1250 62 -1250T56 -1249Q55 -1249 53 -1249T49 -1250Q33 -1250 33 -1239Q33 -1236 50 -1214T98 -1150T163 -1052T238 -910T311 -727Q443 -335 443 251Q443 402 436 532T405 831T339 1142T224 1438T50 1716Q33 1737 33 1741Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-44" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<g transform=“translate(2890,0)”>
<use xlink:href="#E1-MJSZ2-2211" x=“0” y=“0”></use>
<g transform=“translate(147,-1090)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-3D" x=“345” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1124” y=“0”></use>
</g>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“577” y=“1627”></use>
<use xlink:href="#E1-MJSZ4-28" x=“1444” y="-1"></use>
</g>
<g transform=“translate(5127,0)”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-2212" x=“6223” y=“0”></use>
<g transform=“translate(7224,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
<use xlink:href="#E1-MJSZ4-29" x=“7998” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2E" x=“8790” y=“0”></use>
</g>
</svg></p>
<p>Cada termo <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“11.774ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 5069.4 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> d i = a i - b i </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-64” d=“M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1142” y=“0”></use>
<g transform=“translate(2198,0)”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-2212" x=“3294” y=“0”></use>
<g transform=“translate(4295,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
</g>
</svg> tem distribuição:</p>
<ul>
<li>
<svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“23.266ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 10017.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = 1 , b i = 1 ⇒ d i = 0</title>
<defs aria-hidden=“true”>
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<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
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<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1151” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2207” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“2708” y=“0”></use>
<g transform=“translate(3153,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“4205” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“5261” y=“0”></use>
<use xlink:href="#E1-MJMAIN-21D2" x=“6039” y=“0”></use>
<g transform=“translate(7317,0)”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“8460” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“9516” y=“0”></use>
</g>
</svg> (prob 1/4)</li>
<li>
<svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“25.074ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 10795.8 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = 1 , b i = - 1 ⇒ d i = 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”></path>
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<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1151” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2207” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“2708” y=“0”></use>
<g transform=“translate(3153,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“4205” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“5261” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“6039” y=“0”></use>
<use xlink:href="#E1-MJMAIN-21D2" x=“6818” y=“0”></use>
<g transform=“translate(8096,0)”>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“9239” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“10295” y=“0”></use>
</g>
</svg> (prob 1/4)</li>
<li>
<svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“26.882ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 11574.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = - 1 , b i = 1 ⇒ d i = - 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
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<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1151” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“2207” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2986” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“3486” y=“0”></use>
<g transform=“translate(3932,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“4983” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“6039” y=“0”></use>
<use xlink:href="#E1-MJMAIN-21D2" x=“6818” y=“0”></use>
<g transform=“translate(8096,0)”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“9239” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“10295” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“11073” y=“0”></use>
</g>
</svg> (prob 1/4)</li>
<li>
<svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“26.882ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 11574.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = - 1 , b i = - 1 ⇒ d i = 0</title>
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</svg> (prob 1/4)</li>
</ul>
<p>Logo, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.009ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 864.8 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> d i </title>
<defs aria-hidden=“true”>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
</g>
</svg> tem distribuição:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“53.753ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 23143.6 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( d i = 2 ) = 1 / 4 , P ( d i = - 2 ) = 1 / 4 , P ( d i = 0 ) = 1 / 2 .</title>
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<p>A soma <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“14.464ex” height=“3.509ex” style=“vertical-align: -1.005ex;” viewBox=“0 -1078.4 6227.5 1510.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> D N = ∑ i = 1 N d i </title>
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<path stroke-width=“1” id=“E1-MJSZ1-2211” d=“M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-64” d=“M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-44" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<g transform=“translate(2890,0)”>
<use xlink:href="#E1-MJSZ1-2211" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1494” y=“675”></use>
<g transform=“translate(1056,-287)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-3D" x=“345” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1124” y=“0”></use>
</g>
<g transform=“translate(2471,0)”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
</g>
</g>
</g>
</svg> é uma caminhada aleatória com passos 0, +2, -2.Queremos <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“11.431ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 4921.8 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( D N = 0 )</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-44” d=“M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-28" x=“751” y=“0”></use>
<g transform=“translate(1141,0)”>
<use xlink:href="#E1-MJMATHI-44" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“2975” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“4031” y=“0”></use>
<use xlink:href="#E1-MJMAIN-29" x=“4532” y=“0”></use>
</g>
</svg>.</p>
<p>Vamos usar isso pra resolver o problema!</p>
<p>Dois bêbados começam na origem e dão, simultaneamente, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.064ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 888.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
</g>
</svg> passos de mesmo comprimento para direita ou esquerda com probabilidade <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.487ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 1501.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 1 / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMAIN-31" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“500” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1001” y=“0”></use>
</g>
</svg> cada, independentemente um do outro. Queremos a probabilidade de que, após <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.064ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 888.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
</g>
</svg> passos, eles <b>se encontrem</b> novamente (ou seja, estejam na mesma posição).</p>
<p><b>Como vamos resolver isso?</b></p>
<p>Vamos modelar:Seja <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.143ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1353.1 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X n </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6E” d=“M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6E" x=“1171” y="-213"></use>
</g>
</svg> = posição do bêbado 1 após <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.395ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 600.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> n</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6E” d=“M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6E" x=“0” y=“0”></use>
</g>
</svg> passos (passo = ±1).Seja <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.569ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1106.1 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Y n </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6E” d=“M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6E" x=“822” y="-213"></use>
</g>
</svg> = posição do bêbado 2 após <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.395ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 600.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> n</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6E” d=“M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6E" x=“0” y=“0”></use>
</g>
</svg> passos.Ambos começam em 0: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“12.743ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 5486.4 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X 0 = Y 0 = 0</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-30" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1560” y=“0”></use>
<g transform=“translate(2616,0)”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-30" x=“822” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“3929” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“4985” y=“0”></use>
</g>
</svg>.</p>
<p>Os incrementos são independentes entre si e entre os dois bêbados.Eles se encontram após <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.064ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 888.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
</g>
</svg> passos se <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“9.756ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 4200.6 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X N = Y N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<g transform=“translate(2890,0)”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“822” y="-213"></use>
</g>
</g>
</svg>.</p>
<p>Defina <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“16.212ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 6980.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> D N = X N - Y N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-44” d=“M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-44" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<g transform=“translate(2890,0)”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-2212" x=“4669” y=“0”></use>
<g transform=“translate(5670,0)”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“822” y="-213"></use>
</g>
</g>
</svg>. Eles se encontram se <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.877ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3391.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> D N = 0</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-44” d=“M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-44" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“2890” y=“0”></use>
</g>
</svg>.</p>
<p>Note que <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“14.485ex” height=“3.509ex” style=“vertical-align: -1.005ex;” viewBox=“0 -1078.4 6236.5 1510.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X N = ∑ i = 1 N a i </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJSZ1-2211” d=“M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<g transform=“translate(2890,0)”>
<use xlink:href="#E1-MJSZ1-2211" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1494” y=“675”></use>
<g transform=“translate(1056,-287)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-3D" x=“345” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1124” y=“0”></use>
</g>
<g transform=“translate(2471,0)”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
</g>
</g>
</g>
</svg>, onde <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“8.099ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3486.9 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = ± 1</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-B1” d=“M56 320T56 333T70 353H369V502Q369 651 371 655Q376 666 388 666Q402 666 405 654T409 596V500V353H707Q722 345 722 333Q722 320 707 313H409V40H707Q722 32 722 20T707 0H70Q56 7 56 20T70 40H369V313H70Q56 320 56 333Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1151” y=“0”></use>
<use xlink:href="#E1-MJMAIN-B1" x=“2207” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2986” y=“0”></use>
</g>
</svg> com probabilidade 1/2.Analogamente, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“13.679ex” height=“3.509ex” style=“vertical-align: -1.005ex;” viewBox=“0 -1078.4 5889.5 1510.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Y N = ∑ i = 1 N b i </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJSZ1-2211” d=“M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“822” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1587” y=“0”></use>
<g transform=“translate(2643,0)”>
<use xlink:href="#E1-MJSZ1-2211" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1494” y=“675”></use>
<g transform=“translate(1056,-287)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-3D" x=“345” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1124” y=“0”></use>
</g>
<g transform=“translate(2471,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
</g>
</g>
</svg>, com <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.866ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3386.9 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> b i = ± 1</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-B1” d=“M56 320T56 333T70 353H369V502Q369 651 371 655Q376 666 388 666Q402 666 405 654T409 596V500V353H707Q722 345 722 333Q722 320 707 313H409V40H707Q722 32 722 20T707 0H70Q56 7 56 20T70 40H369V313H70Q56 320 56 333Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1051” y=“0”></use>
<use xlink:href="#E1-MJMAIN-B1" x=“2107” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2886” y=“0”></use>
</g>
</svg> com probabilidade 1/2.</p>
<p>Então:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“21.064ex” height=“7.509ex” style=“vertical-align: -3.171ex;” viewBox=“0 -1867.7 9069.4 3233.2” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> D N = ∑ i = 1 N ( a i - b i ) .</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-44” d=“M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJSZ2-2211” d=“M60 948Q63 950 665 950H1267L1325 815Q1384 677 1388 669H1348L1341 683Q1320 724 1285 761Q1235 809 1174 838T1033 881T882 898T699 902H574H543H251L259 891Q722 258 724 252Q725 250 724 246Q721 243 460 -56L196 -356Q196 -357 407 -357Q459 -357 548 -357T676 -358Q812 -358 896 -353T1063 -332T1204 -283T1307 -196Q1328 -170 1348 -124H1388Q1388 -125 1381 -145T1356 -210T1325 -294L1267 -449L666 -450Q64 -450 61 -448Q55 -446 55 -439Q55 -437 57 -433L590 177Q590 178 557 222T452 366T322 544L56 909L55 924Q55 945 60 948Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJSZ4-28” d=“M758 -1237T758 -1240T752 -1249H736Q718 -1249 717 -1248Q711 -1245 672 -1199Q237 -706 237 251T672 1700Q697 1730 716 1749Q718 1750 735 1750H752Q758 1744 758 1741Q758 1737 740 1713T689 1644T619 1537T540 1380T463 1176Q348 802 348 251Q348 -242 441 -599T744 -1218Q758 -1237 758 -1240Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
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<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-44" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<g transform=“translate(2890,0)”>
<use xlink:href="#E1-MJSZ2-2211" x=“0” y=“0”></use>
<g transform=“translate(147,-1090)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-3D" x=“345” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1124” y=“0”></use>
</g>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“577” y=“1627”></use>
<use xlink:href="#E1-MJSZ4-28" x=“1444” y="-1"></use>
</g>
<g transform=“translate(5127,0)”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-2212" x=“6223” y=“0”></use>
<g transform=“translate(7224,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
<use xlink:href="#E1-MJSZ4-29" x=“7998” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2E" x=“8790” y=“0”></use>
</g>
</svg></p>
<p>Cada termo <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“11.774ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 5069.4 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> d i = a i - b i </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-64” d=“M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1142” y=“0”></use>
<g transform=“translate(2198,0)”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-2212" x=“3294” y=“0”></use>
<g transform=“translate(4295,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
</g>
</svg> tem distribuição:</p>
<ul>
<li>
<svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“23.266ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 10017.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = 1 , b i = 1 ⇒ d i = 0</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-21D2” d=“M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-64” d=“M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1151” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2207” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“2708” y=“0”></use>
<g transform=“translate(3153,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“4205” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“5261” y=“0”></use>
<use xlink:href="#E1-MJMAIN-21D2" x=“6039” y=“0”></use>
<g transform=“translate(7317,0)”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“8460” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“9516” y=“0”></use>
</g>
</svg> (prob 1/4)</li>
<li>
<svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“25.074ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 10795.8 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = 1 , b i = - 1 ⇒ d i = 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-21D2” d=“M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z”></path>
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</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1151” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2207” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“2708” y=“0”></use>
<g transform=“translate(3153,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
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</g>
<use xlink:href="#E1-MJMAIN-3D" x=“9239” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“10295” y=“0”></use>
</g>
</svg> (prob 1/4)</li>
<li>
<svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“26.882ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 11574.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = - 1 , b i = 1 ⇒ d i = - 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-21D2” d=“M580 514Q580 525 596 525Q601 525 604 525T609 525T613 524T615 523T617 520T619 517T622 512Q659 438 720 381T831 300T927 263Q944 258 944 250T935 239T898 228T840 204Q696 134 622 -12Q618 -21 615 -22T600 -24Q580 -24 580 -17Q580 -13 585 0Q620 69 671 123L681 133H70Q56 140 56 153Q56 168 72 173H725L735 181Q774 211 852 250Q851 251 834 259T789 283T735 319L725 327H72Q56 332 56 347Q56 360 70 367H681L671 377Q638 412 609 458T580 514Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-64” d=“M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
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</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1151” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“2207” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2986” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“3486” y=“0”></use>
<g transform=“translate(3932,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“4983” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“6039” y=“0”></use>
<use xlink:href="#E1-MJMAIN-21D2" x=“6818” y=“0”></use>
<g transform=“translate(8096,0)”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“9239” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“10295” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“11073” y=“0”></use>
</g>
</svg> (prob 1/4)</li>
<li>
<svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“26.882ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 11574.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = - 1 , b i = - 1 ⇒ d i = 0</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1151” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“2207” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2986” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“3486” y=“0”></use>
<g transform=“translate(3932,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“4983” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“6039” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“6818” y=“0”></use>
<use xlink:href="#E1-MJMAIN-21D2" x=“7596” y=“0”></use>
<g transform=“translate(8874,0)”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“10017” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“11073” y=“0”></use>
</g>
</svg> (prob 1/4)</li>
</ul>
<p>Logo, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.009ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 864.8 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> d i </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-64” d=“M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
</g>
</svg> tem distribuição:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“53.753ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 23143.6 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( d i = 2 ) = 1 / 4 , P ( d i = - 2 ) = 1 / 4 , P ( d i = 0 ) = 1 / 2 .</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
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</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-28" x=“751” y=“0”></use>
<g transform=“translate(1141,0)”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“2283” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“3339” y=“0”></use>
<use xlink:href="#E1-MJMAIN-29" x=“3840” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“4507” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“5563” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“6064” y=“0”></use>
<use xlink:href="#E1-MJMAIN-34" x=“6564” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“7065” y=“0”></use>
<use xlink:href="#E1-MJMATHI-50" x=“7510” y=“0”></use>
<use xlink:href="#E1-MJMAIN-28" x=“8262” y=“0”></use>
<g transform=“translate(8651,0)”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“9794” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“10850” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“11628” y=“0”></use>
<use xlink:href="#E1-MJMAIN-29" x=“12129” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“12796” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“13852” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“14353” y=“0”></use>
<use xlink:href="#E1-MJMAIN-34" x=“14853” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“15354” y=“0”></use>
<use xlink:href="#E1-MJMATHI-50" x=“15799” y=“0”></use>
<use xlink:href="#E1-MJMAIN-28" x=“16551” y=“0”></use>
<g transform=“translate(16940,0)”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“18083” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“19139” y=“0”></use>
<use xlink:href="#E1-MJMAIN-29" x=“19640” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“20307” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“21363” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“21864” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“22364” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2E" x=“22865” y=“0”></use>
</g>
</svg></p>
<p>A soma <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“14.464ex” height=“3.509ex” style=“vertical-align: -1.005ex;” viewBox=“0 -1078.4 6227.5 1510.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> D N = ∑ i = 1 N d i </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-44” d=“M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJSZ1-2211” d=“M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-64” d=“M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-44" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<g transform=“translate(2890,0)”>
<use xlink:href="#E1-MJSZ1-2211" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1494” y=“675”></use>
<g transform=“translate(1056,-287)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-3D" x=“345” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1124” y=“0”></use>
</g>
<g transform=“translate(2471,0)”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
</g>
</g>
</g>
</svg> é uma caminhada aleatória com passos 0, +2, -2.Queremos <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“11.431ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 4921.8 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( D N = 0 )</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-44” d=“M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-28" x=“751” y=“0”></use>
<g transform=“translate(1141,0)”>
<use xlink:href="#E1-MJMATHI-44" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“2975” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“4031” y=“0”></use>
<use xlink:href="#E1-MJMAIN-29" x=“4532” y=“0”></use>
</g>
</svg>.</p>
<p>Vamos usar isso pra resolver o problema!</p>
Passo 2
<p>Podemos transformar:Seja <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> = número de passos onde <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.27ex” height=“2.676ex” style=“vertical-align: -0.838ex;” viewBox=“0 -791.3 2699.4 1152.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> d i ≠ 0</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-64” d=“M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2260” d=“M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
<use xlink:href="#E1-MJMAIN-2260" x=“1142” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“2198” y=“0”></use>
</g>
</svg> (ou seja, onde os bêbados dão passos opostos).Nesses <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> passos, metade são +2 e metade são -2 para que o total seja 0.Além disso, entre os <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.064ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 888.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
</g>
</svg> passos, escolhemos quais são os <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> passos em que <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.27ex” height=“2.676ex” style=“vertical-align: -0.838ex;” viewBox=“0 -791.3 2699.4 1152.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> d i ≠ 0</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-64” d=“M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2260” d=“M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
<use xlink:href="#E1-MJMAIN-2260" x=“1142” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“2198” y=“0”></use>
</g>
</svg>, e depois escolhemos metade deles para serem +2.</p>
<p>Outra abordagem: note que <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.616ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1556.8 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.042ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1309.8 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Y N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“822” y="-213"></use>
</g>
</svg> são independentes e simétricas.Queremos <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“67.318ex” height=“5.176ex” style=“vertical-align: -1.838ex;” viewBox=“0 -1437.2 28984.1 2228.5” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( X N = Y N ) = ∑ k P ( X N = k ) P ( Y N = k ) = ∑ k [ P ( X N = k ) ] 2 </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
<path stroke-width=“1” id=“E1-MJSZ1-2211” d=“M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6B” d=“M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-5B” d=“M118 -250V750H255V710H158V-210H255V-250H118Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-5D” d=“M22 710V750H159V-250H22V-210H119V710H22Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJSZ2-28” d=“M180 96T180 250T205 541T266 770T353 944T444 1069T527 1150H555Q561 1144 561 1141Q561 1137 545 1120T504 1072T447 995T386 878T330 721T288 513T272 251Q272 133 280 56Q293 -87 326 -209T399 -405T475 -531T536 -609T561 -640Q561 -643 555 -649H527Q483 -612 443 -568T353 -443T266 -270T205 -41Z”></path>
<path stroke-width=“1” id=“E1-MJSZ2-29” d=“M35 1138Q35 1150 51 1150H56H69Q113 1113 153 1069T243 944T330 771T391 541T416 250T391 -40T330 -270T243 -443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z”></path>
<path stroke-width=“1” id=“E1-MJSZ2-5D” d=“M16 1099V1150H247V-649H16V-598H196V1099H16Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use xlink:href="#E1-MJSZ2-28" x=“751” y="-1"></use>
<g transform=“translate(1349,0)”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“3183” y=“0”></use>
<g transform=“translate(4239,0)”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“822” y="-213"></use>
</g>
<use xlink:href="#E1-MJSZ2-29" x=“5549” y="-1"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“6424” y=“0”></use>
<g transform=“translate(7481,0)”>
<use xlink:href="#E1-MJSZ1-2211" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6B" x=“1494” y="-405"></use>
<g transform=“translate(1691,0)”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-28" x=“751” y=“0”></use>
</g>
</g>
<g transform=“translate(10314,0)”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“12148” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6B" x=“13204” y=“0”></use>
<use xlink:href="#E1-MJSZ2-29" x=“13726” y="-1"></use>
<use xlink:href="#E1-MJMATHI-50" x=“14323” y=“0”></use>
<use xlink:href="#E1-MJSZ2-28" x=“15075” y="-1"></use>
<g transform=“translate(15672,0)”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“822” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“17260” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6B" x=“18316” y=“0”></use>
<use xlink:href="#E1-MJSZ2-29" x=“18838” y="-1"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“19713” y=“0”></use>
<g transform=“translate(20769,0)”>
<use xlink:href="#E1-MJSZ1-2211" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6B" x=“1494” y="-405"></use>
<g transform=“translate(1691,0)”>
<use xlink:href="#E1-MJMAIN-5B" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMATHI-50" x=“278” y=“0”></use>
<use xlink:href="#E1-MJMAIN-28" x=“1030” y=“0”></use>
</g>
</g>
<g transform=“translate(24047,0)”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“25882” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6B" x=“26938” y=“0”></use>
<use xlink:href="#E1-MJSZ2-29" x=“27460” y="-1"></use>
<g transform=“translate(28057,0)”>
<use xlink:href="#E1-MJSZ2-5D" x=“0” y="-1"></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“668” y=“1240”></use>
</g>
</g>
</svg>.</p>
<p>Como a distribuição de <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.616ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1556.8 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
</svg> é binomial:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“29.254ex” height=“7.509ex” style=“vertical-align: -3.171ex;” viewBox=“0 -1867.7 12595.3 3233.2” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( X N = k ) = N N + k 2 2 - N ,</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6B” d=“M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2B” d=“M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJSZ4-28” d=“M758 -1237T758 -1240T752 -1249H736Q718 -1249 717 -1248Q711 -1245 672 -1199Q237 -706 237 251T672 1700Q697 1730 716 1749Q718 1750 735 1750H752Q758 1744 758 1741Q758 1737 740 1713T689 1644T619 1537T540 1380T463 1176Q348 802 348 251Q348 -242 441 -599T744 -1218Q758 -1237 758 -1240Z”></path>
<path stroke-width=“1” id=“E1-MJSZ4-29” d=“M33 1741Q33 1750 51 1750H60H65Q73 1750 81 1743T119 1700Q554 1207 554 251Q554 -707 119 -1199Q76 -1250 66 -1250Q65 -1250 62 -1250T56 -1249Q55 -1249 53 -1249T49 -1250Q33 -1250 33 -1239Q33 -1236 50 -1214T98 -1150T163 -1052T238 -910T311 -727Q443 -335 443 251Q443 402 436 532T405 831T339 1142T224 1438T50 1716Q33 1737 33 1741Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use xlink:href="#E1-MJSZ4-28" x=“751” y="-1"></use>
<g transform=“translate(1544,0)”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“3378” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6B" x=“4434” y=“0”></use>
<use xlink:href="#E1-MJSZ4-29" x=“4956” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“6026” y=“0”></use>
<g transform=“translate(6805,0)”>
<use xlink:href="#E1-MJSZ4-28"></use>
<g transform=“translate(792,0)”>
<g transform=“translate(120,0)”>
<use xlink:href="#E1-MJMATHI-4E" x=“509” y=“703”></use>
<g transform=“translate(0,-713)”>
<g transform=“translate(120,0)”>
<rect stroke=“none” width=“1667” height=“60” x=“0” y=“220”></rect>
<g transform=“translate(60,503)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2B" x=“888” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6B" x=“1667” y=“0”></use>
</g>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“928” y="-589"></use>
</g>
</g>
</g>
</g>
<use xlink:href="#E1-MJSZ4-29" x=“2940” y=“0”></use>
</g>
<g transform=“translate(10537,0)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<g transform=“translate(500,412)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“778” y=“0”></use>
</g>
</g>
<use xlink:href="#E1-MJMAIN-2C" x=“12316” y=“0”></use>
</g>
</svg></p>
<p>válido para <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.211ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 521.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> k</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6B” d=“M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6B" x=“0” y=“0”></use>
</g>
</svg> tal que <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.115ex” height=“2.343ex” style=“vertical-align: -0.505ex;” viewBox=“0 -791.3 2632.9 1008.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N + k</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2B” d=“M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6B” d=“M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2B" x=“1110” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6B" x=“2111” y=“0”></use>
</g>
</svg> é par (e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.667ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 3301.1 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> ∣ k ∣ ≤ N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-2223” d=“M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z”></path>
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<p>Então:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“34.721ex” height=“7.676ex” style=“vertical-align: -3.338ex;” viewBox=“0 -1867.7 14949.4 3304.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( X N = Y N ) = ∑ j = 0 N N j 2 2 - 2 N ,</title>
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</svg></p>
<p>onde <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“0.985ex” height=“2.509ex” style=“vertical-align: -0.671ex; margin-left: -0.027ex;” viewBox="-11.5 -791.3 424 1080.4" role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> j</title>
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</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6A" x=“0” y=“0”></use>
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</svg> = número de passos à direita do bêbado 1, e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“13.739ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 5915.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X N = 2 j - N</title>
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</svg>.Na soma, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“11.334ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 4880 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> k = 2 j - N</title>
<defs aria-hidden=“true”>
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</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6B" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“799” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1855” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6A" x=“2356” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“2990” y=“0”></use>
<use xlink:href="#E1-MJMATHI-4E" x=“3991” y=“0”></use>
</g>
</svg>, então <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“23.824ex” height=“4.843ex” style=“vertical-align: -1.838ex;” viewBox=“0 -1293.7 10257.6 2085” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( X N = k ) = N j 2 - N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6B” d=“M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z”></path>
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<path stroke-width=“1” id=“E1-MJMATHI-6A” d=“M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z”></path>
<path stroke-width=“1” id=“E1-MJSZ2-28” d=“M180 96T180 250T205 541T266 770T353 944T444 1069T527 1150H555Q561 1144 561 1141Q561 1137 545 1120T504 1072T447 995T386 878T330 721T288 513T272 251Q272 133 280 56Q293 -87 326 -209T399 -405T475 -531T536 -609T561 -640Q561 -643 555 -649H527Q483 -612 443 -568T353 -443T266 -270T205 -41Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
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</defs>
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<use xlink:href="#E1-MJSZ2-28" x=“751” y="-1"></use>
<g transform=“translate(1349,0)”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“3183” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6B" x=“4239” y=“0”></use>
<use xlink:href="#E1-MJSZ2-29" x=“4761” y="-1"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“5636” y=“0”></use>
<g transform=“translate(6415,0)”>
<use xlink:href="#E1-MJSZ2-28"></use>
<g transform=“translate(597,0)”>
<g transform=“translate(120,0)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“0” y=“627”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6A" x=“237” y="-488"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ2-29" x=“1465” y="-1"></use>
</g>
<g transform=“translate(8478,0)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<g transform=“translate(500,393)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“778” y=“0”></use>
</g>
</g>
</g>
</svg>, e a soma sobre <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.211ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 521.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> k</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6B” d=“M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6B" x=“0” y=“0”></use>
</g>
</svg> equivale a somar sobre <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“0.985ex” height=“2.509ex” style=“vertical-align: -0.671ex; margin-left: -0.027ex;” viewBox="-11.5 -791.3 424 1080.4" role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> j</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6A” d=“M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6A" x=“0” y=“0”></use>
</g>
</svg>, com o mesmo binomial para o bêbado 2.</p>
<p>Assim:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“54.668ex” height=“7.676ex” style=“vertical-align: -3.338ex;” viewBox=“0 -1867.7 23537.3 3304.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( encontro ) = ∑ j = 0 N N j 2 - N 2 = 2 - 2 N ∑ j = 0 N N j 2 .</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-65” d=“M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-63” d=“M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-74” d=“M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-72” d=“M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z”></path>
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</defs>
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<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
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<use xlink:href="#E1-MJMAIN-63" x=“1001” y=“0”></use>
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<g transform=“translate(528,0)”>
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<use xlink:href="#E1-MJMATHI-6A" x=“238” y="-686"></use>
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<g transform=“translate(2601,0)”>
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<g transform=“translate(500,412)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“778” y=“0”></use>
</g>
</g>
</g>
<use xlink:href="#E1-MJSZ3-5D" x=“4909” y="-1"></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“7690” y=“1665”></use>
</g>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“15236” y=“0”></use>
<g transform=“translate(16292,0)”>
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<g transform=“translate(500,412)”>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1279” y=“0”></use>
</g>
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<g transform=“translate(18592,0)”>
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<g transform=“translate(124,-1090)”>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-3D" x=“412” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-30" x=“1191” y=“0”></use>
</g>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“577” y=“1627”></use>
<g transform=“translate(1611,0)”>
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<g transform=“translate(736,0)”>
<g transform=“translate(120,0)”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“676”></use>
<use xlink:href="#E1-MJMATHI-6A" x=“238” y="-686"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ3-29" x=“1865” y="-1"></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“3679” y=“1665”></use>
</g>
</g>
<use xlink:href="#E1-MJMAIN-2E" x=“23258” y=“0”></use>
</g>
</svg></p>
<p>Sabemos que <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“19.765ex” height=“5.176ex” style=“vertical-align: -1.838ex;” viewBox=“0 -1437.2 8509.9 2228.5” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> ∑ j = 0 N N j 2 = 2 N N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJSZ1-2211” d=“M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6A” d=“M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
<path stroke-width=“1” id=“E1-MJSZ2-28” d=“M180 96T180 250T205 541T266 770T353 944T444 1069T527 1150H555Q561 1144 561 1141Q561 1137 545 1120T504 1072T447 995T386 878T330 721T288 513T272 251Q272 133 280 56Q293 -87 326 -209T399 -405T475 -531T536 -609T561 -640Q561 -643 555 -649H527Q483 -612 443 -568T353 -443T266 -270T205 -41Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJSZ1-2211" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1494” y=“675”></use>
<g transform=“translate(1056,-287)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6A" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-3D" x=“412” y=“0”></use>
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</g>
<g transform=“translate(2519,0)”>
<use xlink:href="#E1-MJSZ2-28"></use>
<g transform=“translate(597,0)”>
<g transform=“translate(120,0)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“0” y=“627”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6A" x=“237” y="-488"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ2-29" x=“1465” y="-1"></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“2917” y=“1240”></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“5314” y=“0”></use>
<g transform=“translate(6092,0)”>
<use xlink:href="#E1-MJSZ2-28"></use>
<g transform=“translate(597,0)”>
<g transform=“translate(120,0)”>
<g transform=“translate(0,443)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“500” y=“0”></use>
</g>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“250” y="-488"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ2-29" x=“1819” y="-1"></use>
</g>
</g>
</svg>.</p>
<p>Portanto:</p>
<p><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“44.247ex” height=“6.176ex” style=“vertical-align: -2.505ex;” viewBox=“0 -1580.7 19050.7 2659.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( encontro ap o ˊ s N passos ) = 2 - 2 N 2 N N .</title>
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<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
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<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“778” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1279” y=“0”></use>
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<g transform=“translate(15670,0)”>
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<g transform=“translate(120,0)”>
<g transform=“translate(0,676)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMATHI-4E" x=“500” y=“0”></use>
</g>
<use xlink:href="#E1-MJMATHI-4E" x=“250” y="-686"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ3-29" x=“2365” y="-1"></use>
</g>
<use xlink:href="#E1-MJMAIN-2E" x=“18772” y=“0”></use>
</g>
</svg>Tranquilo?</p>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
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<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> = número de passos onde <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.27ex” height=“2.676ex” style=“vertical-align: -0.838ex;” viewBox=“0 -791.3 2699.4 1152.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> d i ≠ 0</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-64” d=“M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2260” d=“M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z”></path>
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</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
<use xlink:href="#E1-MJMAIN-2260" x=“1142” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“2198” y=“0”></use>
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</svg> (ou seja, onde os bêbados dão passos opostos).Nesses <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> passos, metade são +2 e metade são -2 para que o total seja 0.Além disso, entre os <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.064ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 888.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
</g>
</svg> passos, escolhemos quais são os <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> passos em que <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.27ex” height=“2.676ex” style=“vertical-align: -0.838ex;” viewBox=“0 -791.3 2699.4 1152.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> d i ≠ 0</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-64” d=“M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2260” d=“M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-64" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“736” y="-213"></use>
<use xlink:href="#E1-MJMAIN-2260" x=“1142” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“2198” y=“0”></use>
</g>
</svg>, e depois escolhemos metade deles para serem +2.</p>
<p>Outra abordagem: note que <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.616ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1556.8 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.042ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1309.8 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> Y N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“822” y="-213"></use>
</g>
</svg> são independentes e simétricas.Queremos <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“67.318ex” height=“5.176ex” style=“vertical-align: -1.838ex;” viewBox=“0 -1437.2 28984.1 2228.5” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( X N = Y N ) = ∑ k P ( X N = k ) P ( Y N = k ) = ∑ k [ P ( X N = k ) ] 2 </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-59” d=“M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
<path stroke-width=“1” id=“E1-MJSZ1-2211” d=“M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6B” d=“M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-5B” d=“M118 -250V750H255V710H158V-210H255V-250H118Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-5D” d=“M22 710V750H159V-250H22V-210H119V710H22Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJSZ2-28” d=“M180 96T180 250T205 541T266 770T353 944T444 1069T527 1150H555Q561 1144 561 1141Q561 1137 545 1120T504 1072T447 995T386 878T330 721T288 513T272 251Q272 133 280 56Q293 -87 326 -209T399 -405T475 -531T536 -609T561 -640Q561 -643 555 -649H527Q483 -612 443 -568T353 -443T266 -270T205 -41Z”></path>
<path stroke-width=“1” id=“E1-MJSZ2-29” d=“M35 1138Q35 1150 51 1150H56H69Q113 1113 153 1069T243 944T330 771T391 541T416 250T391 -40T330 -270T243 -443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z”></path>
<path stroke-width=“1” id=“E1-MJSZ2-5D” d=“M16 1099V1150H247V-649H16V-598H196V1099H16Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use xlink:href="#E1-MJSZ2-28" x=“751” y="-1"></use>
<g transform=“translate(1349,0)”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“3183” y=“0”></use>
<g transform=“translate(4239,0)”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“822” y="-213"></use>
</g>
<use xlink:href="#E1-MJSZ2-29" x=“5549” y="-1"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“6424” y=“0”></use>
<g transform=“translate(7481,0)”>
<use xlink:href="#E1-MJSZ1-2211" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6B" x=“1494” y="-405"></use>
<g transform=“translate(1691,0)”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-28" x=“751” y=“0”></use>
</g>
</g>
<g transform=“translate(10314,0)”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“12148” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6B" x=“13204” y=“0”></use>
<use xlink:href="#E1-MJSZ2-29" x=“13726” y="-1"></use>
<use xlink:href="#E1-MJMATHI-50" x=“14323” y=“0”></use>
<use xlink:href="#E1-MJSZ2-28" x=“15075” y="-1"></use>
<g transform=“translate(15672,0)”>
<use xlink:href="#E1-MJMATHI-59" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“822” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“17260” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6B" x=“18316” y=“0”></use>
<use xlink:href="#E1-MJSZ2-29" x=“18838” y="-1"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“19713” y=“0”></use>
<g transform=“translate(20769,0)”>
<use xlink:href="#E1-MJSZ1-2211" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6B" x=“1494” y="-405"></use>
<g transform=“translate(1691,0)”>
<use xlink:href="#E1-MJMAIN-5B" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMATHI-50" x=“278” y=“0”></use>
<use xlink:href="#E1-MJMAIN-28" x=“1030” y=“0”></use>
</g>
</g>
<g transform=“translate(24047,0)”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“25882” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6B" x=“26938” y=“0”></use>
<use xlink:href="#E1-MJSZ2-29" x=“27460” y="-1"></use>
<g transform=“translate(28057,0)”>
<use xlink:href="#E1-MJSZ2-5D" x=“0” y="-1"></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“668” y=“1240”></use>
</g>
</g>
</svg>.</p>
<p>Como a distribuição de <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.616ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1556.8 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
</svg> é binomial:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“29.254ex” height=“7.509ex” style=“vertical-align: -3.171ex;” viewBox=“0 -1867.7 12595.3 3233.2” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( X N = k ) = N N + k 2 2 - N ,</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-58” d=“M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6B” d=“M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJSZ4-28” d=“M758 -1237T758 -1240T752 -1249H736Q718 -1249 717 -1248Q711 -1245 672 -1199Q237 -706 237 251T672 1700Q697 1730 716 1749Q718 1750 735 1750H752Q758 1744 758 1741Q758 1737 740 1713T689 1644T619 1537T540 1380T463 1176Q348 802 348 251Q348 -242 441 -599T744 -1218Q758 -1237 758 -1240Z”></path>
<path stroke-width=“1” id=“E1-MJSZ4-29” d=“M33 1741Q33 1750 51 1750H60H65Q73 1750 81 1743T119 1700Q554 1207 554 251Q554 -707 119 -1199Q76 -1250 66 -1250Q65 -1250 62 -1250T56 -1249Q55 -1249 53 -1249T49 -1250Q33 -1250 33 -1239Q33 -1236 50 -1214T98 -1150T163 -1052T238 -910T311 -727Q443 -335 443 251Q443 402 436 532T405 831T339 1142T224 1438T50 1716Q33 1737 33 1741Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”></path>
</defs>
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<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use xlink:href="#E1-MJSZ4-28" x=“751” y="-1"></use>
<g transform=“translate(1544,0)”>
<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“3378” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6B" x=“4434” y=“0”></use>
<use xlink:href="#E1-MJSZ4-29" x=“4956” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“6026” y=“0”></use>
<g transform=“translate(6805,0)”>
<use xlink:href="#E1-MJSZ4-28"></use>
<g transform=“translate(792,0)”>
<g transform=“translate(120,0)”>
<use xlink:href="#E1-MJMATHI-4E" x=“509” y=“703”></use>
<g transform=“translate(0,-713)”>
<g transform=“translate(120,0)”>
<rect stroke=“none” width=“1667” height=“60” x=“0” y=“220”></rect>
<g transform=“translate(60,503)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2B" x=“888” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6B" x=“1667” y=“0”></use>
</g>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“928” y="-589"></use>
</g>
</g>
</g>
</g>
<use xlink:href="#E1-MJSZ4-29" x=“2940” y=“0”></use>
</g>
<g transform=“translate(10537,0)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<g transform=“translate(500,412)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“778” y=“0”></use>
</g>
</g>
<use xlink:href="#E1-MJMAIN-2C" x=“12316” y=“0”></use>
</g>
</svg></p>
<p>válido para <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.211ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 521.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> k</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6B” d=“M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6B" x=“0” y=“0”></use>
</g>
</svg> tal que <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.115ex” height=“2.343ex” style=“vertical-align: -0.505ex;” viewBox=“0 -791.3 2632.9 1008.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N + k</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2B” d=“M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6B” d=“M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2B" x=“1110” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6B" x=“2111” y=“0”></use>
</g>
</svg> é par (e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.667ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 3301.1 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> ∣ k ∣ ≤ N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-2223” d=“M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6B” d=“M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2264” d=“M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMAIN-2223" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6B" x=“278” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2223" x=“1077” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2264" x=“1356” y=“0”></use>
<use xlink:href="#E1-MJMATHI-4E" x=“2412” y=“0”></use>
</g>
</svg>).</p>
<p>Então:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“34.721ex” height=“7.676ex” style=“vertical-align: -3.338ex;” viewBox=“0 -1867.7 14949.4 3304.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( X N = Y N ) = ∑ j = 0 N N j 2 2 - 2 N ,</title>
<defs aria-hidden=“true”>
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<p>onde <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“0.985ex” height=“2.509ex” style=“vertical-align: -0.671ex; margin-left: -0.027ex;” viewBox="-11.5 -791.3 424 1080.4" role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> j</title>
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<path stroke-width=“1” id=“E1-MJMATHI-6A” d=“M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z”></path>
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<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6A" x=“0” y=“0”></use>
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</svg> = número de passos à direita do bêbado 1, e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“13.739ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 5915.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> X N = 2 j - N</title>
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<use xlink:href="#E1-MJMATHI-58" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“2890” y=“0”></use>
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</svg>.Na soma, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“11.334ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 4880 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> k = 2 j - N</title>
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</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6B" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“799” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1855” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6A" x=“2356” y=“0”></use>
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<use xlink:href="#E1-MJMATHI-4E" x=“3991” y=“0”></use>
</g>
</svg>, então <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“23.824ex” height=“4.843ex” style=“vertical-align: -1.838ex;” viewBox=“0 -1293.7 10257.6 2085” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( X N = k ) = N j 2 - N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
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<path stroke-width=“1” id=“E1-MJMATHI-6B” d=“M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z”></path>
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<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use xlink:href="#E1-MJSZ2-28" x=“751” y="-1"></use>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
</g>
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<use xlink:href="#E1-MJSZ2-29" x=“4761” y="-1"></use>
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<g transform=“translate(6415,0)”>
<use xlink:href="#E1-MJSZ2-28"></use>
<g transform=“translate(597,0)”>
<g transform=“translate(120,0)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“0” y=“627”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6A" x=“237” y="-488"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ2-29" x=“1465” y="-1"></use>
</g>
<g transform=“translate(8478,0)”>
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<g transform=“translate(500,393)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“778” y=“0”></use>
</g>
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</g>
</svg>, e a soma sobre <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.211ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 521.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> k</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6B” d=“M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6B" x=“0” y=“0”></use>
</g>
</svg> equivale a somar sobre <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“0.985ex” height=“2.509ex” style=“vertical-align: -0.671ex; margin-left: -0.027ex;” viewBox="-11.5 -791.3 424 1080.4" role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> j</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6A” d=“M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6A" x=“0” y=“0”></use>
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</svg>, com o mesmo binomial para o bêbado 2.</p>
<p>Assim:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“54.668ex” height=“7.676ex” style=“vertical-align: -3.338ex;” viewBox=“0 -1867.7 23537.3 3304.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( encontro ) = ∑ j = 0 N N j 2 - N 2 = 2 - 2 N ∑ j = 0 N N j 2 .</title>
<defs aria-hidden=“true”>
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<path stroke-width=“1” id=“E1-MJSZ2-2211” d=“M60 948Q63 950 665 950H1267L1325 815Q1384 677 1388 669H1348L1341 683Q1320 724 1285 761Q1235 809 1174 838T1033 881T882 898T699 902H574H543H251L259 891Q722 258 724 252Q725 250 724 246Q721 243 460 -56L196 -356Q196 -357 407 -357Q459 -357 548 -357T676 -358Q812 -358 896 -353T1063 -332T1204 -283T1307 -196Q1328 -170 1348 -124H1388Q1388 -125 1381 -145T1356 -210T1325 -294L1267 -449L666 -450Q64 -450 61 -448Q55 -446 55 -439Q55 -437 57 -433L590 177Q590 178 557 222T452 366T322 544L56 909L55 924Q55 945 60 948Z”></path>
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</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use xlink:href="#E1-MJSZ4-28" x=“751” y="-1"></use>
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<use xlink:href="#E1-MJMAIN-6E" x=“444” y=“0”></use>
<use xlink:href="#E1-MJMAIN-63" x=“1001” y=“0”></use>
<use xlink:href="#E1-MJMAIN-6F" x=“1445” y=“0”></use>
<use xlink:href="#E1-MJMAIN-6E" x=“1946” y=“0”></use>
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</g>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-3D" x=“412” y=“0”></use>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“577” y=“1627”></use>
<g transform=“translate(1611,0)”>
<use xlink:href="#E1-MJSZ3-5B"></use>
<g transform=“translate(528,0)”>
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<g transform=“translate(736,0)”>
<g transform=“translate(120,0)”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“676”></use>
<use xlink:href="#E1-MJMATHI-6A" x=“238” y="-686"></use>
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</g>
<use xlink:href="#E1-MJSZ3-29" x=“1865” y="-1"></use>
<g transform=“translate(2601,0)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<g transform=“translate(500,412)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“778” y=“0”></use>
</g>
</g>
</g>
<use xlink:href="#E1-MJSZ3-5D" x=“4909” y="-1"></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“7690” y=“1665”></use>
</g>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“15236” y=“0”></use>
<g transform=“translate(16292,0)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<g transform=“translate(500,412)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“778” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1279” y=“0”></use>
</g>
</g>
<g transform=“translate(18592,0)”>
<use xlink:href="#E1-MJSZ2-2211" x=“0” y=“0”></use>
<g transform=“translate(124,-1090)”>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-3D" x=“412” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-30" x=“1191” y=“0”></use>
</g>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“577” y=“1627”></use>
<g transform=“translate(1611,0)”>
<use xlink:href="#E1-MJSZ3-28"></use>
<g transform=“translate(736,0)”>
<g transform=“translate(120,0)”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“676”></use>
<use xlink:href="#E1-MJMATHI-6A" x=“238” y="-686"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ3-29" x=“1865” y="-1"></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“3679” y=“1665”></use>
</g>
</g>
<use xlink:href="#E1-MJMAIN-2E" x=“23258” y=“0”></use>
</g>
</svg></p>
<p>Sabemos que <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“19.765ex” height=“5.176ex” style=“vertical-align: -1.838ex;” viewBox=“0 -1437.2 8509.9 2228.5” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> ∑ j = 0 N N j 2 = 2 N N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJSZ1-2211” d=“M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6A” d=“M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
<path stroke-width=“1” id=“E1-MJSZ2-28” d=“M180 96T180 250T205 541T266 770T353 944T444 1069T527 1150H555Q561 1144 561 1141Q561 1137 545 1120T504 1072T447 995T386 878T330 721T288 513T272 251Q272 133 280 56Q293 -87 326 -209T399 -405T475 -531T536 -609T561 -640Q561 -643 555 -649H527Q483 -612 443 -568T353 -443T266 -270T205 -41Z”></path>
<path stroke-width=“1” id=“E1-MJSZ2-29” d=“M35 1138Q35 1150 51 1150H56H69Q113 1113 153 1069T243 944T330 771T391 541T416 250T391 -40T330 -270T243 -443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJSZ1-2211" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1494” y=“675”></use>
<g transform=“translate(1056,-287)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6A" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-3D" x=“412” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-30" x=“1191” y=“0”></use>
</g>
<g transform=“translate(2519,0)”>
<use xlink:href="#E1-MJSZ2-28"></use>
<g transform=“translate(597,0)”>
<g transform=“translate(120,0)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“0” y=“627”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6A" x=“237” y="-488"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ2-29" x=“1465” y="-1"></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“2917” y=“1240”></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“5314” y=“0”></use>
<g transform=“translate(6092,0)”>
<use xlink:href="#E1-MJSZ2-28"></use>
<g transform=“translate(597,0)”>
<g transform=“translate(120,0)”>
<g transform=“translate(0,443)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“500” y=“0”></use>
</g>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“250” y="-488"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ2-29" x=“1819” y="-1"></use>
</g>
</g>
</svg>.</p>
<p>Portanto:</p>
<p><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“44.247ex” height=“6.176ex” style=“vertical-align: -2.505ex;” viewBox=“0 -1580.7 19050.7 2659.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( encontro ap o ˊ s N passos ) = 2 - 2 N 2 N N .</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-63” d=“M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-6F” d=“M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-74” d=“M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z”></path>
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<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
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<g transform=“translate(1488,0)”>
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<use xlink:href="#E1-MJMAIN-6E" x=“444” y=“0”></use>
<use xlink:href="#E1-MJMAIN-63" x=“1001” y=“0”></use>
<use xlink:href="#E1-MJMAIN-6F" x=“1445” y=“0”></use>
<use xlink:href="#E1-MJMAIN-6E" x=“1946” y=“0”></use>
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<use xlink:href="#E1-MJMAIN-61" x=“2201” y=“0”></use>
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<use xlink:href="#E1-MJMAIN-73" x=“3096” y=“0”></use>
<use xlink:href="#E1-MJMAIN-6F" x=“3491” y=“0”></use>
<use xlink:href="#E1-MJMAIN-73" x=“3991” y=“0”></use>
</g>
<use xlink:href="#E1-MJSZ3-29" x=“11466” y="-1"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“12480” y=“0”></use>
<g transform=“translate(13537,0)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<g transform=“translate(500,412)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“778” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1279” y=“0”></use>
</g>
</g>
<g transform=“translate(15670,0)”>
<use xlink:href="#E1-MJSZ3-28"></use>
<g transform=“translate(736,0)”>
<g transform=“translate(120,0)”>
<g transform=“translate(0,676)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMATHI-4E" x=“500” y=“0”></use>
</g>
<use xlink:href="#E1-MJMATHI-4E" x=“250” y="-686"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ3-29" x=“2365” y="-1"></use>
</g>
<use xlink:href="#E1-MJMAIN-2E" x=“18772” y=“0”></use>
</g>
</svg>Tranquilo?</p>
Passo 3
<p>Seja <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> = número de passos em que os dois dão passos opostos (um para direita, outro para esquerda).Para que <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.877ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3391.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> D N = 0</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-44” d=“M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-44" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“2890” y=“0”></use>
</g>
</svg>, desses <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> passos opostos, exatamente <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“4.365ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 1879.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“878” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1379” y=“0”></use>
</g>
</svg> devem ser com <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“16.999ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 7318.9 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = + 1 , b i = - 1</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2B” d=“M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1151” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2B" x=“2207” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2986” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“3486” y=“0”></use>
<g transform=“translate(3932,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“4983” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“6039” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“6818” y=“0”></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“4.365ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 1879.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“878” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1379” y=“0”></use>
</g>
</svg> com <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“16.999ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 7318.9 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = - 1 , b i = + 1</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2B” d=“M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1151” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“2207” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2986” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“3486” y=“0”></use>
<g transform=“translate(3932,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“4983” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2B" x=“6039” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“6818” y=“0”></use>
</g>
</svg>.Além disso, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> deve ser par.</p>
<p>Probabilidade de um passo ser oposto: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“22.213ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 9563.9 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 2 × ( 1 / 2 × 1 / 2 ) = 1 / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-D7” d=“M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-D7" x=“722” y=“0”></use>
<use xlink:href="#E1-MJMAIN-28" x=“1723” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2112” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“2613” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“3113” y=“0”></use>
<use xlink:href="#E1-MJMAIN-D7" x=“3836” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“4837” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“5337” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“5838” y=“0”></use>
<use xlink:href="#E1-MJMAIN-29" x=“6338” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“7006” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“8062” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“8562” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“9063” y=“0”></use>
</g>
</svg>.Probabilidade de um passo ser igual (ambos direita ou ambos esquerda): <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.487ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 1501.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 1 / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMAIN-31" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“500” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1001” y=“0”></use>
</g>
</svg>.</p>
<p>Então, a probabilidade de termos <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> passos opostos entre <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.064ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 888.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
</g>
</svg> é binomial:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“39.222ex” height=“6.676ex” style=“vertical-align: -2.505ex;” viewBox=“0 -1796 16887.2 2874.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N m ( 1 / 2 ) m ( 1 / 2 ) N - m = N m 2 - N .</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
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<path stroke-width=“1” id=“E1-MJSZ3-29” d=“M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2E” d=“M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
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<g transform=“translate(736,0)”>
<g transform=“translate(120,0)”>
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<use xlink:href="#E1-MJMATHI-6D" x=“5” y="-686"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ3-29" x=“1865” y="-1"></use>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6D" x=“1667” y=“0”></use>
</g>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“11449” y=“0”></use>
<g transform=“translate(12227,0)”>
<use xlink:href="#E1-MJSZ3-28"></use>
<g transform=“translate(736,0)”>
<g transform=“translate(120,0)”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“676”></use>
<use xlink:href="#E1-MJMATHI-6D" x=“5” y="-686"></use>
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</g>
<use xlink:href="#E1-MJSZ3-29" x=“1865” y="-1"></use>
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<g transform=“translate(14829,0)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<g transform=“translate(500,412)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“778” y=“0”></use>
</g>
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<use xlink:href="#E1-MJMAIN-2E" x=“16608” y=“0”></use>
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</svg></p>
<p>Dado <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> passos opostos, a probabilidade de que exatamente <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“4.365ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 1879.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“878” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1379” y=“0”></use>
</g>
</svg> sejam do tipo (+,-) e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“4.365ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 1879.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“878” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1379” y=“0”></use>
</g>
</svg> do tipo (-,+) é:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“13.107ex” height=“6.176ex” style=“vertical-align: -2.505ex;” viewBox=“0 -1580.7 5643.2 2659.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m m / 2 2 - m .</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
<path stroke-width=“1” id=“E1-MJSZ3-28” d=“M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z”></path>
<path stroke-width=“1” id=“E1-MJSZ3-29” d=“M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2E” d=“M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJSZ3-28"></use>
<g transform=“translate(736,0)”>
<g transform=“translate(120,0)”>
<use xlink:href="#E1-MJMATHI-6D" x=“500” y=“676”></use>
<g transform=“translate(0,-686)”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“878” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1379” y=“0”></use>
</g>
</g>
</g>
<use xlink:href="#E1-MJSZ3-29" x=“2856” y="-1"></use>
<g transform=“translate(3592,0)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<g transform=“translate(500,412)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6D" x=“778” y=“0”></use>
</g>
</g>
<use xlink:href="#E1-MJMAIN-2E" x=“5364” y=“0”></use>
</g>
</svg></p>
<p>Assim,</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“46.387ex” height=“13.509ex” style=“vertical-align: -6.171ex;” viewBox=“0 -3159.4 19972.2 5816.5” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( D N = 0 ) = ∑ m = 0 m p a r N N m 2 - N ⋅ m m / 2 2 - m .</title>
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<p>Fazendo <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.513ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3234.6 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m = 2 k</title>
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<title> P = 2 - N ∑ k = 0 N / 2 N 2 k 2 k k 2 - 2 k .</title>
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<p>Esta soma é igual a <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“10.569ex” height=“4.843ex” style=“vertical-align: -1.838ex;” viewBox=“0 -1293.7 4550.3 2085” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 2 - 2 N 2 N N </title>
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<g transform=“translate(500,393)”>
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<g transform=“translate(597,0)”>
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<g transform=“translate(0,443)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“250” y="-488"></use>
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<use xlink:href="#E1-MJSZ2-29" x=“1819” y="-1"></use>
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</svg>, conforme identidade combinatória conhecida.</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“17.003ex” height=“6.176ex” style=“vertical-align: -2.505ex;” viewBox=“0 -1580.7 7320.7 2659.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P = 2 - 2 N 2 N N </title>
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<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
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<use xlink:href="#E1-MJMATHI-4E" x=“500” y=“0”></use>
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<use xlink:href="#E1-MJMATHI-4E" x=“250” y="-686"></use>
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</g>
</g>
</svg></p>
<p>É isso! O que achou? Responde Aí!</p>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> = número de passos em que os dois dão passos opostos (um para direita, outro para esquerda).Para que <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.877ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3391.3 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> D N = 0</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-44” d=“M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-44" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1171” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1834” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“2890” y=“0”></use>
</g>
</svg>, desses <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> passos opostos, exatamente <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“4.365ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 1879.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“878” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1379” y=“0”></use>
</g>
</svg> devem ser com <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“16.999ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 7318.9 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = + 1 , b i = - 1</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2B” d=“M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1151” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2B" x=“2207” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2986” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“3486” y=“0”></use>
<g transform=“translate(3932,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“4983” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“6039” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“6818” y=“0”></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“4.365ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 1879.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“878” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1379” y=“0”></use>
</g>
</svg> com <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“16.999ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 7318.9 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> a i = - 1 , b i = + 1</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-61” d=“M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-69” d=“M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2C” d=“M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2B” d=“M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-61" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“748” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1151” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“2207” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2986” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2C" x=“3486” y=“0”></use>
<g transform=“translate(3932,0)”>
<use xlink:href="#E1-MJMATHI-62" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-69" x=“607” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“4983” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2B" x=“6039” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“6818” y=“0”></use>
</g>
</svg>.Além disso, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> deve ser par.</p>
<p>Probabilidade de um passo ser oposto: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“22.213ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 9563.9 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 2 × ( 1 / 2 × 1 / 2 ) = 1 / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-D7” d=“M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-D7" x=“722” y=“0”></use>
<use xlink:href="#E1-MJMAIN-28" x=“1723” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“2112” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“2613” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“3113” y=“0”></use>
<use xlink:href="#E1-MJMAIN-D7" x=“3836” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“4837” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“5337” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“5838” y=“0”></use>
<use xlink:href="#E1-MJMAIN-29" x=“6338” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“7006” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“8062” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“8562” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“9063” y=“0”></use>
</g>
</svg>.Probabilidade de um passo ser igual (ambos direita ou ambos esquerda): <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.487ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 1501.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 1 / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMAIN-31" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“500” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1001” y=“0”></use>
</g>
</svg>.</p>
<p>Então, a probabilidade de termos <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> passos opostos entre <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.064ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 888.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
</g>
</svg> é binomial:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“39.222ex” height=“6.676ex” style=“vertical-align: -2.505ex;” viewBox=“0 -1796 16887.2 2874.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N m ( 1 / 2 ) m ( 1 / 2 ) N - m = N m 2 - N .</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
<path stroke-width=“1” id=“E1-MJSZ3-28” d=“M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z”></path>
<path stroke-width=“1” id=“E1-MJSZ3-29” d=“M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2E” d=“M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJSZ3-28"></use>
<g transform=“translate(736,0)”>
<g transform=“translate(120,0)”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“676”></use>
<use xlink:href="#E1-MJMATHI-6D" x=“5” y="-686"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ3-29" x=“1865” y="-1"></use>
<use xlink:href="#E1-MJSZ3-28" x=“2601” y="-1"></use>
<use xlink:href="#E1-MJMAIN-31" x=“3338” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“3838” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“4339” y=“0”></use>
<g transform=“translate(4839,0)”>
<use xlink:href="#E1-MJSZ3-29" x=“0” y="-1"></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6D" x=“1041” y=“1665”></use>
</g>
<use xlink:href="#E1-MJSZ3-28" x=“6297” y="-1"></use>
<use xlink:href="#E1-MJMAIN-31" x=“7033” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“7534” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“8034” y=“0”></use>
<g transform=“translate(8535,0)”>
<use xlink:href="#E1-MJSZ3-29" x=“0” y="-1"></use>
<g transform=“translate(736,1177)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“888” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6D" x=“1667” y=“0”></use>
</g>
</g>
<use xlink:href="#E1-MJMAIN-3D" x=“11449” y=“0”></use>
<g transform=“translate(12227,0)”>
<use xlink:href="#E1-MJSZ3-28"></use>
<g transform=“translate(736,0)”>
<g transform=“translate(120,0)”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“676”></use>
<use xlink:href="#E1-MJMATHI-6D" x=“5” y="-686"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ3-29" x=“1865” y="-1"></use>
</g>
<g transform=“translate(14829,0)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<g transform=“translate(500,412)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“778” y=“0”></use>
</g>
</g>
<use xlink:href="#E1-MJMAIN-2E" x=“16608” y=“0”></use>
</g>
</svg></p>
<p>Dado <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.04ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 878.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
</g>
</svg> passos opostos, a probabilidade de que exatamente <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“4.365ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 1879.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
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<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“878” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1379” y=“0”></use>
</g>
</svg> sejam do tipo (+,-) e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“4.365ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 1879.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m / 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
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<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“878” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1379” y=“0”></use>
</g>
</svg> do tipo (-,+) é:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“13.107ex” height=“6.176ex” style=“vertical-align: -2.505ex;” viewBox=“0 -1580.7 5643.2 2659.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m m / 2 2 - m .</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-6D” d=“M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
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<path stroke-width=“1” id=“E1-MJSZ3-29” d=“M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
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</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJSZ3-28"></use>
<g transform=“translate(736,0)”>
<g transform=“translate(120,0)”>
<use xlink:href="#E1-MJMATHI-6D" x=“500” y=“676”></use>
<g transform=“translate(0,-686)”>
<use xlink:href="#E1-MJMATHI-6D" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“878” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1379” y=“0”></use>
</g>
</g>
</g>
<use xlink:href="#E1-MJSZ3-29" x=“2856” y="-1"></use>
<g transform=“translate(3592,0)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<g transform=“translate(500,412)”>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-6D" x=“778” y=“0”></use>
</g>
</g>
<use xlink:href="#E1-MJMAIN-2E" x=“5364” y=“0”></use>
</g>
</svg></p>
<p>Assim,</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“46.387ex” height=“13.509ex” style=“vertical-align: -6.171ex;” viewBox=“0 -3159.4 19972.2 5816.5” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P ( D N = 0 ) = ∑ m = 0 m p a r N N m 2 - N ⋅ m m / 2 2 - m .</title>
<defs aria-hidden=“true”>
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<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
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<path stroke-width=“1” id=“E1-MJSZ2-2211” d=“M60 948Q63 950 665 950H1267L1325 815Q1384 677 1388 669H1348L1341 683Q1320 724 1285 761Q1235 809 1174 838T1033 881T882 898T699 902H574H543H251L259 891Q722 258 724 252Q725 250 724 246Q721 243 460 -56L196 -356Q196 -357 407 -357Q459 -357 548 -357T676 -358Q812 -358 896 -353T1063 -332T1204 -283T1307 -196Q1328 -170 1348 -124H1388Q1388 -125 1381 -145T1356 -210T1325 -294L1267 -449L666 -450Q64 -450 61 -448Q55 -446 55 -439Q55 -437 57 -433L590 177Q590 178 557 222T452 366T322 544L56 909L55 924Q55 945 60 948Z”></path>
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<path stroke-width=“1” id=“E1-MJSZ3-29” d=“M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z”></path>
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<use xlink:href="#E1-MJMAIN-2F" x=“878” y=“0”></use>
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</svg></p>
<p>Fazendo <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.513ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3234.6 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> m = 2 k</title>
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<use xlink:href="#E1-MJMAIN-3D" x=“1156” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“2212” y=“0”></use>
<use xlink:href="#E1-MJMATHI-6B" x=“2713” y=“0”></use>
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</svg>,</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“31.63ex” height=“7.843ex” style=“vertical-align: -3.171ex;” viewBox=“0 -2011.3 13618.3 3376.7” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P = 2 - N ∑ k = 0 N / 2 N 2 k 2 k k 2 - 2 k .</title>
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</svg></p>
<p>Esta soma é igual a <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“10.569ex” height=“4.843ex” style=“vertical-align: -1.838ex;” viewBox=“0 -1293.7 4550.3 2085” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 2 - 2 N 2 N N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
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<path stroke-width=“1” id=“E1-MJSZ2-28” d=“M180 96T180 250T205 541T266 770T353 944T444 1069T527 1150H555Q561 1144 561 1141Q561 1137 545 1120T504 1072T447 995T386 878T330 721T288 513T272 251Q272 133 280 56Q293 -87 326 -209T399 -405T475 -531T536 -609T561 -640Q561 -643 555 -649H527Q483 -612 443 -568T353 -443T266 -270T205 -41Z”></path>
<path stroke-width=“1” id=“E1-MJSZ2-29” d=“M35 1138Q35 1150 51 1150H56H69Q113 1113 153 1069T243 944T330 771T391 541T416 250T391 -40T330 -270T243 -443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z”></path>
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<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
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<g transform=“translate(500,393)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“778” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1279” y=“0”></use>
</g>
<g transform=“translate(2133,0)”>
<use xlink:href="#E1-MJSZ2-28"></use>
<g transform=“translate(597,0)”>
<g transform=“translate(120,0)”>
<g transform=“translate(0,443)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“500” y=“0”></use>
</g>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“250” y="-488"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ2-29" x=“1819” y="-1"></use>
</g>
</g>
</svg>, conforme identidade combinatória conhecida.</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“17.003ex” height=“6.176ex” style=“vertical-align: -2.505ex;” viewBox=“0 -1580.7 7320.7 2659.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P = 2 - 2 N 2 N N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
<path stroke-width=“1” id=“E1-MJSZ3-28” d=“M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z”></path>
<path stroke-width=“1” id=“E1-MJSZ3-29” d=“M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1029” y=“0”></use>
<g transform=“translate(2085,0)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<g transform=“translate(500,412)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“778” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1279” y=“0”></use>
</g>
</g>
<g transform=“translate(4218,0)”>
<use xlink:href="#E1-MJSZ3-28"></use>
<g transform=“translate(736,0)”>
<g transform=“translate(120,0)”>
<g transform=“translate(0,676)”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMATHI-4E" x=“500” y=“0”></use>
</g>
<use xlink:href="#E1-MJMATHI-4E" x=“250” y="-686"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ3-29" x=“2365” y="-1"></use>
</g>
</g>
</svg></p>
<p>É isso! O que achou? Responde Aí!</p>
Resposta
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“12.159ex” height=“6.176ex” style=“vertical-align: -2.505ex;” viewBox=“0 -1580.7 5235.2 2659.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 2 - 2 N 2 N N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
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<path stroke-width=“1” id=“E1-MJSZ3-29” d=“M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z”></path>
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<g transform=“translate(500,412)”>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-2212" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“778” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“1279” y=“0”></use>
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<use xlink:href="#E1-MJMATHI-4E" x=“500” y=“0”></use>
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<use xlink:href="#E1-MJMATHI-4E" x=“250” y="-686"></use>
</g>
</g>
<use xlink:href="#E1-MJSZ3-29" x=“2365” y="-1"></use>
</g>
</g>
</svg></p>
<title> 2 - 2 N 2 N N </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
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</svg></p>