Monty Hall Matsala

Ka yi kokarin fahimtar na dogon lokaci a sa mamaki wuyar warwarewa, da aka buga shekaru 23 da suka wuce a cikin mujallar "Parade Magazine", kuma ya zama wani irin amsa kuwwa daga cikin shahararrun American show "Bari mu yi Deal" (fassara). The aiki na tushen tsaye Monty Hall paradox.

Ka yi kokarin mayar da events aka bayyana. Tunanin kanka a jam'iyyar da aka gudanar yayin da show. Kana ya kai ga uku ƙõfõfi, kuma ta samar da ikon saka daya kawai, jawo hankalin cewa kyaututtuka suna boye a baya kowane kofa. Babban kyauta ne da mabuɗan zuwa alatu mota da ka tara, idan ka bude "daidai" kofa ga sauran kofofi boye consolation kyaututtuka, su zama daidai - domin a goat. Hakika, a consolation kyauta ba za ka zama mai farin ciki - ka sha'awa a cikin babban kyauta.

Bayan yawa tunani, ku rashin qarfin zuciya aya ga daya daga cikin kofofin (misali, da farko). Wannan ne paradox na Monty Hall, ku haƙĩƙa, ba su sani ba, don haka kawai fatan for abubuwa da cewa mu'ujizai har yanzu faru wani lokacin.

Amma manyan dalilin buɗewa da ba daidai ba kofa, wanda ya yanke shawarar nuna muku da sauran (ya san daidai inda aka boye Kunamu). Kuma ya buɗe ƙofar, bayan da ya boye cikin goat. Alal misali, na uku. Mai gabatarwa simplifies da aiki na samar domin zabin ne yanzu kawai biyu kofofin. Haka kuma, shi yayi karin lokaci zuwa zaton da kuma sa kiran wani ƙyaure, idan kun yi shakka.

Kara damar karba makullin, idan ka canza tunani da kuma shigar a kan wani kofa? Tunanin wani minti daya. Abin da zai tsaya?

A daidai amsar da aka bude wani kofa, ku ƙara chances na yin ninkininki key. Shakka? Mutane da yawa shakka. Amma daidai wannan ne Monty Hall paradox.

A bayani na paradox kamar haka. Bari mu ce ka zabi yanzu na farko kofa. Mun wakiltar kofofin a cikin nau'i na biyu dabi'u (dabi'u). The darajar A, bari na farko (zaba kawai ka) kofa, da kuma darajar B - sauran kofofi. Yiwuwar ingress makullin a A ne 1/3, da kuma yiwuwar samun na biyu key darajar B ne daidai to, bi da bi, 2/3. Kada ku yarda? Next. Idan kana da damar da za su bude wani biyu da kuma na uku kofa, ya jingina a cikin ni'imar da dabi'u na B, chances tafi da mota zai zama sau biyu a matsayin mai yawa.

Bari mu bincika wannan more a hankali. Ka tabbata da cewa akwai haƙĩƙa, an A goat (a kalla daya) da kuma yiwu makullin. Bude daya kofa baya, kamar, da halin da ake ciki bai canza: har yanzu kasance yiwuwa guda biyu: lashe mota da kuma lashe a goat. Amma mayar da hankali a kan darajar B, yiwuwar samun nasara, ka har yanzu kara zuwa 2/3, tun for yawa A yiwuwa ne kawai 1/3.

Wani, riga mai Schematic, misali:

G1 g2 g3 canza selection ba tare da canza selection
to To To To don
To ga kyau ga da kyau
To da kyau da kyau zuwa ga

inda d1 - na farko kofa, D2 - na biyu kofa, g3 - da uku kofa, Well - dabba (goat), don - keys (da mota).

Wasu Kada ku riƙi Monty Hall paradox tsanani, jayayya da cewa yiwuwar samun lashe key shi ne har yanzu 50/50 ( "ko dai-ko"). Amma reusable tabbaci har yanzu ya tabbatar da ka'idar yana da wani m hakkin ya wanzu da kuma aiki a 2/3 daga cikin lokuta na duka gabatar. Alal misali, talatin gabatar damar zuwa wasa za ka iya samun madaidaicin amsar a ashirin. Kuma wannan shi ne quite a high yawan.

Kuma sau da yawa da Monty Hall paradox amfani da 'yan wasa da fare a kan caca, ko wasa cards. Don me ba su rasa? Amsar ne bayyananne: zari ne ruining. Ko tashin hankali. Kamar yadda kuke so. Bayan cire tukunya, da ɗan wasa ne ba su iya dakatar da haukan ji da kuma yin wani fare, riga ya manta game da ka'idar. Amma da asarar ba a soke ta. Shi ne kashi na nufin samun riba.

Monty Hall ya tabbatar da cewa bayan bude kofa da akuya wasan ne ko da yaushe mafi riba don canja farko zabi, saboda chances na har yanzu kara. Ga irin wannan a nan su ne, da paradoxes ka'idar yiwuwa.

Idan bayani da ya rage m zuwa gare ku, kokarin watsi dai wadannan muhawara da kuma tabbatar da ka'idar ilimin kididdiga (ko, idan kuka so, gwaje, a jerin gwaje-gwajen). Irin wannan ilmin lissafi shi ne ko da yaushe m. Good luck!