[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"transcript-75c57b50-7073-4fb7-9fd4-def8d48f62cb-en":3,"footer-top-topics-en":321,"transcript-poster-75c57b50-7073-4fb7-9fd4-def8d48f62cb":374,"footer-top-speakers-en":375},{"falas":4,"lang":308,"meta":309},[5,15,22,29,36,43,50,56,62,69,74,79,85,90,96,102,108,114,120,125,132,137,144,150,156,162,167,172,178,185,191,197,203,209,215,221,227,232,238,244,250,256,261,267,273,279,285,290,296,302],{"idx":6,"utterance_id":7,"speaker_name":8,"speaker_slug":9,"text":10,"start_s":11,"end_s":12,"word_count":13,"indexable":14},0,"42643","Tarcisio","tarcisio","Folks, let's address a very important topic during World Cup time.",0.22,3.34,14,false,{"idx":16,"utterance_id":17,"speaker_name":8,"speaker_slug":9,"text":18,"start_s":19,"end_s":20,"word_count":21,"indexable":14},1,"42644","The World Cup sticker album.",4.28,5.66,6,{"idx":23,"utterance_id":24,"speaker_name":8,"speaker_slug":9,"text":25,"start_s":26,"end_s":27,"word_count":28,"indexable":14},2,"42645","My challenge today is a different challenge — the World Cup challenge.",6.68,9.18,12,{"idx":30,"utterance_id":31,"speaker_name":8,"speaker_slug":9,"text":32,"start_s":33,"end_s":34,"word_count":35,"indexable":14},3,"42646","And I want to know how much we need to spend to complete the World Cup album without trading any stickers.",9.36,16.62,20,{"idx":37,"utterance_id":38,"speaker_name":8,"speaker_slug":9,"text":39,"start_s":40,"end_s":41,"word_count":42,"indexable":14},4,"42647","And for that I initially need to know how many stickers our album has.",16.92,20.86,18,{"idx":44,"utterance_id":45,"speaker_name":8,"speaker_slug":9,"text":46,"start_s":47,"end_s":48,"word_count":49,"indexable":14},5,"42648","I'll call it n and n is equal to 980.",21.16,22.98,10,{"idx":21,"utterance_id":51,"speaker_name":8,"speaker_slug":9,"text":52,"start_s":53,"end_s":54,"word_count":55,"indexable":14},"42649","The World Cup album has 980 stickers.",23.54,25.4,7,{"idx":55,"utterance_id":57,"speaker_name":8,"speaker_slug":9,"text":58,"start_s":59,"end_s":60,"word_count":61,"indexable":14},"42650","Let's use probability and statistics to help us.",25.56,28.66,9,{"idx":63,"utterance_id":64,"speaker_name":8,"speaker_slug":9,"text":65,"start_s":66,"end_s":67,"word_count":68,"indexable":14},8,"42651","If I don't have any stickers and I'm going to take my first sticker, what's the probability that I get a sticker that I don't yet have?",28.92,34.74,26,{"idx":61,"utterance_id":70,"speaker_name":8,"speaker_slug":9,"text":71,"start_s":72,"end_s":73,"word_count":44,"indexable":14},"42652","The probability is exactly 1.",34.88,37.16,{"idx":49,"utterance_id":75,"speaker_name":8,"speaker_slug":9,"text":76,"start_s":77,"end_s":78,"word_count":44,"indexable":14},"42653","I don't have any stickers.",37.32,38.26,{"idx":80,"utterance_id":81,"speaker_name":8,"speaker_slug":9,"text":82,"start_s":83,"end_s":84,"word_count":80,"indexable":14},11,"42654","I'll certainly draw a sticker I don't have.",38.48,40.62,{"idx":28,"utterance_id":86,"speaker_name":8,"speaker_slug":9,"text":87,"start_s":88,"end_s":89,"word_count":63,"indexable":14},"42655","Now I'm getting to the very end of the album.",40.92,42.84,{"idx":91,"utterance_id":92,"speaker_name":8,"speaker_slug":9,"text":93,"start_s":94,"end_s":95,"word_count":37,"indexable":14},13,"42656","I already have 979 stickers.",43.04,45.66,{"idx":13,"utterance_id":97,"speaker_name":8,"speaker_slug":9,"text":98,"start_s":99,"end_s":100,"word_count":101,"indexable":14},"42657","What is the probability, assuming that the probability of drawing any sticker is the same, that I draw exactly the sticker I need?",45.82,52.34,25,{"idx":103,"utterance_id":104,"speaker_name":8,"speaker_slug":9,"text":105,"start_s":106,"end_s":107,"word_count":55,"indexable":14},15,"42658","And I'll call this P980.",52.46,53.28,{"idx":109,"utterance_id":110,"speaker_name":8,"speaker_slug":9,"text":111,"start_s":112,"end_s":113,"word_count":55,"indexable":14},16,"42659","This probability will be 1 over 980.",55.1,57.32,{"idx":115,"utterance_id":116,"speaker_name":8,"speaker_slug":9,"text":117,"start_s":118,"end_s":119,"word_count":35,"indexable":14},17,"42660","What is the probability that I draw, then, the sticker I need, knowing that I already have K stickers?",59.02,64.9,{"idx":42,"utterance_id":121,"speaker_name":8,"speaker_slug":9,"text":122,"start_s":123,"end_s":124,"word_count":103,"indexable":14},"42661","That probability will be... n minus k over n. And that is important information.",65.1,71.32,{"idx":126,"utterance_id":127,"speaker_name":8,"speaker_slug":9,"text":128,"start_s":129,"end_s":130,"word_count":131,"indexable":14},19,"42662","Because if I know that the probability of getting a sticker I don't yet have, given I have k stickers, is this, how many times will I have to repeat an event to draw exactly the sticker I want?",71.48,81.74,41,{"idx":35,"utterance_id":133,"speaker_name":8,"speaker_slug":9,"text":134,"start_s":135,"end_s":136,"word_count":37,"indexable":14},"42663","The inverse of the probability.",82,83.5,{"idx":138,"utterance_id":139,"speaker_name":8,"speaker_slug":9,"text":140,"start_s":141,"end_s":142,"word_count":143,"indexable":14},21,"42664","That is, 1 over p or n over n minus k. Knowing the number of events I need to perform to draw that sticker I need, it's possible to calculate the total number of stickers I'll need, which will be the sum of those events.",83.66,97.56,46,{"idx":145,"utterance_id":146,"speaker_name":8,"speaker_slug":9,"text":147,"start_s":148,"end_s":149,"word_count":28,"indexable":14},22,"42665","So Q — I'll call this Q — will be equal to",97.68,100.24,{"idx":151,"utterance_id":152,"speaker_name":8,"speaker_slug":9,"text":153,"start_s":154,"end_s":155,"word_count":61,"indexable":14},23,"42666","When K is zero, N over N, plus",100.4,103.3,{"idx":157,"utterance_id":158,"speaker_name":8,"speaker_slug":9,"text":159,"start_s":160,"end_s":161,"word_count":55,"indexable":14},24,"42667","In the next event, I'll already have one sticker.",103.5,105.02,{"idx":101,"utterance_id":163,"speaker_name":8,"speaker_slug":9,"text":164,"start_s":165,"end_s":166,"word_count":109,"indexable":14},"42668","How many times will I have to repeat this event to draw the sticker I need?",105.18,108.5,{"idx":68,"utterance_id":168,"speaker_name":8,"speaker_slug":9,"text":169,"start_s":170,"end_s":171,"word_count":151,"indexable":14},"42669","N over N minus 1, plus N over N minus 2, plus, and so on, up to N over 2, plus N over 1.",108.96,119,{"idx":173,"utterance_id":174,"speaker_name":8,"speaker_slug":9,"text":175,"start_s":176,"end_s":177,"word_count":63,"indexable":14},27,"42670","So here, notice that the n repeats.",119.68,121.68,{"idx":179,"utterance_id":180,"speaker_name":8,"speaker_slug":9,"text":181,"start_s":182,"end_s":183,"word_count":184,"indexable":14},28,"42671","I'll factor out the n, so my total will be the n that multiplies 1 over n, plus 1 over n minus 1, plus 1 over n minus 2, plus 1 over 2.",122.16,135.14,36,{"idx":186,"utterance_id":187,"speaker_name":8,"speaker_slug":9,"text":188,"start_s":189,"end_s":190,"word_count":23,"indexable":14},29,"42672","Plus 1.",135.56,136.34,{"idx":192,"utterance_id":193,"speaker_name":8,"speaker_slug":9,"text":194,"start_s":195,"end_s":196,"word_count":13,"indexable":14},30,"42673","And the sum of this harmonic series can be calculated as follows.",136.58,140.86,{"idx":198,"utterance_id":199,"speaker_name":8,"speaker_slug":9,"text":200,"start_s":201,"end_s":202,"word_count":61,"indexable":14},31,"42674","Approximately the natural log of n plus a constant.",141.66,146.44,{"idx":204,"utterance_id":205,"speaker_name":8,"speaker_slug":9,"text":206,"start_s":207,"end_s":208,"word_count":61,"indexable":14},32,"42675","This constant is very common in number theory.",146.9,148.92,{"idx":210,"utterance_id":211,"speaker_name":8,"speaker_slug":9,"text":212,"start_s":213,"end_s":214,"word_count":44,"indexable":14},33,"42676","It is called the Euler-Mascheroni constant.",148.96,151.16,{"idx":216,"utterance_id":217,"speaker_name":8,"speaker_slug":9,"text":218,"start_s":219,"end_s":220,"word_count":42,"indexable":14},34,"42677","And it can be defined as the limit of the difference between the natural logarithm and the harmonic series.",151.8,162.08,{"idx":222,"utterance_id":223,"speaker_name":8,"speaker_slug":9,"text":224,"start_s":225,"end_s":226,"word_count":21,"indexable":14},35,"42678","And it has an approximate value here.",162.6,164.72,{"idx":184,"utterance_id":228,"speaker_name":8,"speaker_slug":9,"text":229,"start_s":230,"end_s":231,"word_count":23,"indexable":14},"42679","of 0.58.",165.28,166.54,{"idx":233,"utterance_id":234,"speaker_name":8,"speaker_slug":9,"text":235,"start_s":236,"end_s":237,"word_count":80,"indexable":14},37,"42680","Knowing that, I can now calculate my number of stickers.",167.72,171.86,{"idx":239,"utterance_id":240,"speaker_name":8,"speaker_slug":9,"text":241,"start_s":242,"end_s":243,"word_count":138,"indexable":14},38,"42681","And my number of stickers will be N, which is 980, times the natural logarithm of 980 plus 0.58.",172.3,180.78,{"idx":245,"utterance_id":246,"speaker_name":8,"speaker_slug":9,"text":247,"start_s":248,"end_s":249,"word_count":63,"indexable":14},39,"42682","Natural logarithm of 980, more or less 6.88.",183.4,185.9,{"idx":251,"utterance_id":252,"speaker_name":8,"speaker_slug":9,"text":253,"start_s":254,"end_s":255,"word_count":115,"indexable":14},40,"42683","So we will have here that this will be 980 times 6.88 plus 0.58.",186.04,194.18,{"idx":131,"utterance_id":257,"speaker_name":8,"speaker_slug":9,"text":258,"start_s":259,"end_s":260,"word_count":37,"indexable":14},"42684","That gives 7.46.",195.48,196.7,{"idx":262,"utterance_id":263,"speaker_name":8,"speaker_slug":9,"text":264,"start_s":265,"end_s":266,"word_count":55,"indexable":14},42,"42685","And that multiplied by 980 is approximately 7,311.",199.34,203.3,{"idx":268,"utterance_id":269,"speaker_name":8,"speaker_slug":9,"text":270,"start_s":271,"end_s":272,"word_count":63,"indexable":14},43,"42686","So, that's my number of stickers.",205.94,208.44,{"idx":274,"utterance_id":275,"speaker_name":8,"speaker_slug":9,"text":276,"start_s":277,"end_s":278,"word_count":145,"indexable":14},44,"42687","I will have to repeat the event 7,311 times to guarantee that I'll have the 980 stickers without making any trades.",208.68,216.8,{"idx":280,"utterance_id":281,"speaker_name":8,"speaker_slug":9,"text":282,"start_s":283,"end_s":284,"word_count":49,"indexable":14},45,"42688","Since each sticker costs one real, I will need to spend",216.88,220.08,{"idx":143,"utterance_id":286,"speaker_name":8,"speaker_slug":9,"text":287,"start_s":288,"end_s":289,"word_count":23,"indexable":14},"42689","R$ 7,311.",223.26,223.3,{"idx":291,"utterance_id":292,"speaker_name":8,"speaker_slug":9,"text":293,"start_s":294,"end_s":295,"word_count":21,"indexable":14},47,"42690","Knowing that, what's the tip?",224.32,226.46,{"idx":297,"utterance_id":298,"speaker_name":8,"speaker_slug":9,"text":299,"start_s":300,"end_s":301,"word_count":23,"indexable":14},48,"42691","Trade stickers.",226.68,227.62,{"idx":303,"utterance_id":304,"speaker_name":8,"speaker_slug":9,"text":305,"start_s":306,"end_s":307,"word_count":198,"indexable":14},49,"42692","You can go to the park, to the mall, with your parents, with your friends, talk a lot, talk about the World Cup, trade stickers and save a lot of money.",227.82,241.1,"en",{"job_id":310,"title":311,"source_url":312,"platform":313,"content_type":314,"published_at":315,"duration_sec":316,"n_classified":317,"speakers":318},"75c57b50-7073-4fb7-9fd4-def8d48f62cb","Tarcísio Gomes de Freitas - Figurinha repetida de novo? Calma! Vamos resolver isso daí.  No Desaf...","https:\u002F\u002Fx.com\u002Ftarcisiogdf\u002Fstatus\u002F2068653797434368377","twitter","video","2026-06-21T11:14:33Z",241.116,50,[319],{"name":8,"slug":9,"photo_url":320,"n_falas":317},"\u002Fprofiles\u002Ftarcisio\u002Fphoto.png",{"limit":49,"offset":6,"topics":322,"total":373},[323,328,333,338,343,348,353,358,363,368],{"label":324,"n_speakers":68,"n_utterances":325,"n_videos":326,"slug":327},"National Security",2695,190,"seguranca-nacional",{"label":329,"n_speakers":204,"n_utterances":330,"n_videos":331,"slug":332},"Education",1685,229,"educacao",{"label":334,"n_speakers":151,"n_utterances":335,"n_videos":336,"slug":337},"Public Safety and Order",1580,244,"seguranca-publica-e-ordem",{"label":339,"n_speakers":210,"n_utterances":340,"n_videos":341,"slug":342},"Combating Impunity",1469,292,"combate-a-impunidade",{"label":344,"n_speakers":204,"n_utterances":345,"n_videos":346,"slug":347},"Monetary 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