{"id":8167,"date":"2026-09-09T01:26:14","date_gmt":"2026-09-08T22:26:14","guid":{"rendered":"https:\/\/www.schooler.org.ua\/jak-pratsjuye-binomnij-rozpodil-vid-kidkiv-kubika-do-gorohu-mendelja\/"},"modified":"2026-09-09T01:26:14","modified_gmt":"2026-09-08T22:26:14","slug":"jak-pratsjuye-binomnij-rozpodil-vid-kidkiv-kubika-do-gorohu-mendelja","status":"publish","type":"post","link":"https:\/\/www.schooler.org.ua\/cs\/jak-funguje-binomicke-rozdeleni-od-hodu-kostkou-po-mendeluv-hrasek\/","title":{"rendered":"Jak funguje binomick\u00e9 rozd\u011blen\u00ed: od hod\u016f kostkou po Mendel\u016fv hr\u00e1\u0161ek"},"content":{"rendered":"

Binomick\u00e9 rozd\u011blen\u00ed je statistick\u00fd z\u00e1klad. Pom\u00e1h\u00e1 p\u0159edpov\u00eddat v\u00fdsledky v situac\u00edch, kdy je po\u010det pokus\u016f pevn\u00fd a pravd\u011bpodobnost \u00fasp\u011bchu v ka\u017ed\u00e9m pokusu je stejn\u00e1. <\/p>\n

P\u0159edstavte si to jako matematiku za ot\u00e1zkou: “Jak\u00e9 jsou \u0161ance?” <\/p>\n

Tento model plat\u00ed pro diskr\u00e9tn\u00ed procesy. Pravidla jsou zde p\u0159\u00edsn\u00e1. Pot\u0159ebujete pevn\u00fd po\u010det pokus\u016f. Ka\u017ed\u00fd test mus\u00ed b\u00fdt nez\u00e1visl\u00fd. Pravd\u011bpodobnost \u00fasp\u011bchu mus\u00ed z\u016fstat konstantn\u00ed. Pokud je alespo\u0148 jedna z t\u011bchto podm\u00ednek poru\u0161ena, binomick\u00fd model p\u0159estane fungovat. <\/p>\n

Vzniklo v hazardn\u00edch hr\u00e1ch. Jacob Bernoulli to formalizoval v roce 1713. Jeho d\u016fkaz byl publikov\u00e1n posmrtn\u011b. Uk\u00e1zal, \u017ee pravd\u011bpodobnost dosa\u017een\u00ed p\u0159esn\u011b k<\/em> \u00fasp\u011bch\u016f na n<\/em> pokusech odpov\u00edd\u00e1 k<\/em> -t\u00e9mu \u010dlenu expanze (p + q)^n<\/em>. Zde p<\/em> je pravd\u011bpodobnost \u00fasp\u011bchu. q<\/em> je pravd\u011bpodobnost selh\u00e1n\u00ed, kter\u00e1 se rovn\u00e1 1 – p<\/em>. <\/p>\n

Pr\u00e1v\u011b z tohoto rozkladu poch\u00e1z\u00ed n\u00e1zev. Dva term\u00edny. Povznesena k moci. Binomick\u00fd. <\/p>\n

Pod\u00edvejme se na konkr\u00e9tn\u00ed p\u0159\u00edklad. Hod\u00edte kostkou 50kr\u00e1t. Mus\u00edte zn\u00e1t pravd\u011bpodobnost, \u017ee \u0161estka padne p\u0159esn\u011b 10kr\u00e1t. <\/p>\n

Pravd\u011bpodobnost hodu \u0161estky je 1\/6. Pravd\u011bpodobnost, \u017ee nepadne \u0161estka, je 5\/6. Tak\u017ee p<\/em> = 1\/6 a q<\/em> = 5\/6. Vzorec bere v \u00favahu 10. \u010dlen (po\u010d\u00edt\u00e1no od nuly) roz\u0161\u00ed\u0159en\u00ed (5\/6 + 1\/6)^50<\/em>. <\/p>\n

V\u00fdsledek je p\u0159ibli\u017en\u011b 0,1156. Asi 11,5 %. Nen\u00ed to ojedin\u011bl\u00e1 ud\u00e1lost, ale ani zaru\u010dena. <\/p>\n

To nen\u00ed jen teorie. To je praxe. Ukazuje, jak pravd\u011bpodobn\u00e9 jsou konkr\u00e9tn\u00ed v\u00fdsledky, kdy\u017e se ud\u00e1losti opakuj\u00ed. <\/p>\n

Kontroverze o Mendelovi<\/h3>\n

V roce 1936 Ronald Fisher pou\u017eil tento n\u00e1stroj ke zpochybn\u011bn\u00ed jednoho z nejslavn\u011bj\u0161\u00edch jmen ve v\u011bd\u011b. Gregor Mendel publikoval sv\u00e9 pokusy o genetice hrachu v roce 1866. Staly se z\u00e1kladem modern\u00ed genetiky. <\/p>\n

Fisher znovu analyzoval Mendelova data pomoc\u00ed binomick\u00e9ho rozd\u011blen\u00ed. Mendelovy z\u00e1kony d\u011bdi\u010dnosti p\u0159edpov\u00eddaly, \u017ee 3\/4 potomk\u016f v dan\u00e9m k\u0159\u00ed\u017een\u00ed bude m\u00edt semena \u017elut\u00e9ho hrachu. <\/p>\n

Mendel napo\u010d\u00edtal v jednom pokusu 8 023 hrach\u016f. O\u010dek\u00e1van\u00fd pr\u016fm\u011brn\u00fd po\u010det \u017elut\u00fdch hr\u00e1ch\u016f by byl asi 6 017. Mendel ohl\u00e1sil 6 022 \u017elut\u00fdch hrach\u016f. <\/p>\n

Je to neuv\u011b\u0159iteln\u011b bl\u00edzko. <\/p>\n

Fisher vypo\u010d\u00edtal pravd\u011bpodobnost takov\u00e9 n\u00e1hody. Stalo se to asi 1x z 10x. To vypad\u00e1 podez\u0159ele dob\u0159e. <\/p>\n

Mendel m\u011bl sedm r\u016fzn\u00fdch experiment\u016f. V\u0161echny se t\u00e9m\u011b\u0159 dokonale shodovaly s o\u010dek\u00e1van\u00fdmi hodnotami binomick\u00e9ho rozd\u011blen\u00ed. Jeden z nich m\u011bl dokonce lehkou mendelovskou v\u00fdpo\u010detn\u00ed chybu, ale kone\u010dn\u00fd v\u00fdsledek i tak modelu p\u0159\u00edli\u0161 sed\u011bl. <\/p>\n

Fischer sv\u00e1 zji\u0161t\u011bn\u00ed zve\u0159ejnil. Nazna\u010doval v\u011bdeck\u00e9 fal\u0161ov\u00e1n\u00ed. Zm\u011bnil Mendel sv\u00e1 data, aby odpov\u00eddala teorii? Debata pokra\u010duje. Nikdo podvod p\u0159esv\u011bd\u010div\u011b neprok\u00e1zal. Statistick\u00e1 anom\u00e1lie ale z\u016fst\u00e1v\u00e1. <\/p>\n

Pro\u010d je to pro v\u00e1s d\u016fle\u017eit\u00e9?<\/h3>\n

Pochopen\u00ed binomick\u00e9ho rozd\u011blen\u00ed pom\u00e1h\u00e1 identifikovat vzory. Pom\u00e1h\u00e1 odd\u011blit \u0161t\u011bst\u00ed od dovednost\u00ed. Pom\u016f\u017ee v\u00e1m to pochopit, kdy data vypadaj\u00ed \u201ep\u0159\u00edli\u0161 dob\u0159e na to, aby to byla pravda\u201c. <\/p>\n

Pou\u017e\u00edv\u00e1te jej v\u017edy, kdy\u017e hodnot\u00edte riziko v opakuj\u00edc\u00edch se ud\u00e1lostech. <\/p>\n

    \n
  • Hozen\u00ed minc\u00ed<\/strong> : Kolik hlav z\u00edsk\u00e1te za 100 hod\u016f? <\/li>\n
  • Kontrola kvality<\/strong> : Kolik vadn\u00fdch v\u00fdrobk\u016f je v d\u00e1vce 1 000 kus\u016f? <\/li>\n
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    Matematika z\u016fst\u00e1v\u00e1 stejn\u00e1. Kontext se m\u011bn\u00ed. <\/p>\n

    Kl\u00ed\u010dem je v\u011bd\u011bt, kdy to pou\u017e\u00edt. Pot\u0159ebujete nez\u00e1vislost. Chcete pevnou pravd\u011bpodobnost. Pot\u0159ebujete ur\u010dit\u00fd po\u010det pokus\u016f. <\/p>\n

    Pokud jsou tyto podm\u00ednky spln\u011bny, binom<\/p>\n","protected":false},"excerpt":{"rendered":"

    Binomick\u00e9 rozd\u011blen\u00ed je statistick\u00fd z\u00e1klad. Pom\u00e1h\u00e1 p\u0159edpov\u00eddat v\u00fdsledky v situac\u00edch, kdy je po\u010det pokus\u016f pevn\u00fd a pravd\u011bpodobnost \u00fasp\u011bchu v ka\u017ed\u00e9m pokusu je stejn\u00e1. P\u0159edstavte si to jako matematiku za ot\u00e1zkou: “Jak\u00e9 jsou \u0161ance?” Tento model plat\u00ed pro diskr\u00e9tn\u00ed procesy. Pravidla jsou zde p\u0159\u00edsn\u00e1. Pot\u0159ebujete pevn\u00fd po\u010det pokus\u016f. Ka\u017ed\u00fd test mus\u00ed b\u00fdt nez\u00e1visl\u00fd. Pravd\u011bpodobnost \u00fasp\u011bchu mus\u00ed […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":""},"categories":[50],"tags":[],"wpm_language_slugs":{"cs":"jak-funguje-binomicke-rozdeleni-od-hodu-kostkou-po-mendeluv-hrasek","de":"so-funktioniert-die-binomialverteilung-von-wurfelwurfen-bis-zu-mendels","en":"how-binomial-distribution-works-from-dice-rolls-to-mendels-peas","es":"como-funciona-la-distribucion-binomial-de-las-tiradas-de-dados-a-los","fr":"comment-fonctionne-la-distribution-binomiale-des-lancers-de-des-aux","id":"cara-kerja-distribusi-binomial-dari-gulungan-dadu-hingga-kacang-mendel","it":"come-funziona-la-distribuzione-binomiale-dai-lanci-di-dadi-ai","nl":"hoe-binomiale-distributie-werkt-van-dobbelsteenworpen-tot-mendels-peas","pl":"jak-dziala-rozklad-dwumianowy-od-rzutu-kostka-do-groszku-mendla","pt":"como-funciona-a-distribuicao-binomial-dos-lancamentos-de-dados-as","ru-ru":"kak-rabotaet-binomialnoe-raspredelenie-ot-broskov-kubika-do-goroha","uk-ua":"jak-pratsjuye-binomnij-rozpodil-vid-kidkiv-kubika-do-gorohu-mendelja"},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts\/8167"}],"collection":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/comments?post=8167"}],"version-history":[{"count":0,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts\/8167\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/media?parent=8167"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/categories?post=8167"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/tags?post=8167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}