Monty Hall Dhibaatada

Isku day inaad si ay u fahmaan muddo dheer xujo cajiib ah, la daabacay 23 sano ka hor in majaladda "Parade Magazine" oo uu noqday nooc ka mid ah echo of show caanka American "ha Deal ee ka dhig" (turjumay). Joogtada ah hawl-ku-saleysan Monty Hall liddiga.

Isku day inaad si loo soo celiyo dhacdooyinka tilmaamay. Naftaada Imagine xaflad lagu qabtay halka show ah. Waxaad keentay in saddex albaabada iyo siiyaan awood u leeyahay inuu sheeg mid kaliya, ka digay in abaal-marinno ku qarsoon yihiin albaab kasta. Abaalmarinta ugu weyn waa furaha gaariga raaxada ah in aad soo qaado, haddii aad furo "sax" albaabka u albaabada haray qariyey abaalmarino tacsida, si sax noqon - for riyo ah. Dabcan, abaalmarinta tacsida ah aanad ku farxi doonaan - aad xiisaynayso abaalmarinta grand.

Ka dib markii Fikir badan, aad dhibic go'aan jilicsan in mid ka mid ah albaabada (tusaale ahaan, marka hore ka). Taasi waa isku liddiga ah ee Monty Hall, sida xaqiiqada ah aadan aqoon, oo sidaas daraaddeed rajaynaynaa oo keliya, waayo, waxyaalaha qaar cajaa'ibyo sameeya weli mararka qaarkood dhici.

Laakiin sababta keentay xaarraysa qaldan, oo ay go'aansatay in ay aad iyo kuwa kale oo farta (uu ogyahay meesha saxda Qarsoona Furayaasha). Iyo albaabka, ka danbeeya oo qariyey orgiga uu furmo. Tusaale ahaan, kii saddexaad. Idaaciga nayaa hawsha siinaya doorashada ee hadda jira laba albaab oo kaliya. Waxaa intaa dheer, waxa ay bixisaa waqti dheeraad ah in ay ka fekeraan oo u saamaxaaya in ay soo wac albaabka kale, haddii aad wax shaki ah.

Kordhi fursad ay ku soo qaado furayaasha, haddii aad maskaxdaada beddesho, kana gala albaabka kale? Daqiiqad ka feker. Maxaa joojin doonaa?

Jawaabta saxda ah waxaa furitaanka albaabka kale, aad badsatid fursada is muhiimka ah Laab. Shaki? Shaki badan ayaa. Laakiin si hufan, kanu waa liddiga Monty Hall.

Sharaxa of liddiga ah sida soo socota. Aynu idinku hadda dooran albaabka marka hore. Waxaan wakiil albaabbadii oo qaab laba qiimeeyo (qiimaha). Qiimaha A, kii hore ha (kaliya aad dooratay) albaabka, iyo qiimaha B - albaabbadii haray. furayaasha ingress itimaalka in A waa 1/3, oo suurto gal ah lagaa labaad qiimaha B muhiimka ah waa loo siman yahay si, siday u kala horreeyaan, 2/3. Ma ku raacsan? Next. Haddii aad fursad u leeyihiin in la furo labaad iyo saddexaad albaab, tiirsan ay guushu ku qiyamka B, fursadaha tago baabuur by noqon lahaa laba jeer ka badan.

Ina keena aynu baari this more si dhow ula. Ma hubtaa in ay jiraan dhab ahaan waa inaad orgi ah A (ugu yaraan hal) oo suurto gal ah furayaasha. Furitaanka mid albaabka marka laga reebo, sida, xaalada aysan waxba ka beddelin, weli laba suurtagal: baabuur ku guuleystay iyo guuleysan riyo ah. Laakiin diiradda qiimaha B, jaaniska of guusha, waxaad weli u kordhiyo si 2/3, tan iyo for tiro itimaalka A waa 1/3 kaliya.

Kale, mar hore schematic ah, tusaale ahaan:

G3 g2 G1 beddelo doorashada oo aan badalayn doorashada
si Well Well Well in
Well in ay si fiican u Well
Well Well Well in ay

halkaas oo D1 - albaabka marka hore, D2 - albaabka labaad, G3 - albaab saddexaad, Waa hagaag - xoolaha (ariga), waayo, - furaha (gaariga).

Qaar ka mid ah ha ka yeelanina liddiga Monty Hall si dhab ah, ku dooday in jaaniska ah guusha muhiimka ah ee weli waa 50/50 ( "midkood-ama"). Laakiin xaqiijinta karo weli Oo Xaqiijiyay In aragtida ah wuxuu xaq u leeyahay macquul ah si uu u jiro iyo ka shaqeeya 2/3 oo ka mid ah kiisaska oo dhan soo bandhigay. Tusaale ahaan, soddon soo bandhigay fursado ay ku ciyaaraan waxaad awoodi doontaa inaad si aad u hesho jawaabta saxda ah ee labaatan noqon doonaa. Oo kanu waa arrin boqolkiiba sare.

Oo marar badan ay isku liddiga Monty Hall isticmaalo ciyaartoyda by sharad roulette, ama turub. Maxaad ay lumiyo? Jawaabtu waa cadahay: damac waxaa ku qariyaan. Ama farax. Sida aad rabto. Ka dib markii ay ka saareen dherigii, ciyaaryahanka mar dambe waa inay awoodaan inay joojiyaan dareenka Cadho iyo ka dhigi bet kale, mar hore waxaan halmaamay ku saabsan aragtida ah. Laakiin khasaare ma ayaa la baajiyay. Waa boqolleyda abaalmarinta.

Monty Hall uu xaqiijinayaa in ka dib markii albaabka furitaanka ciyaarta riyo ah had iyo jeer waa faa'iido dheeraad ah in la beddelo doorashada hore, sababtoo ah fursadaha weli sii kordhaya. Halkan sida halkan ay yihiin, isburintii ka aragti ah itimaalka.

Haddii sharaxaad weli kala cadeyn in aad, isku day in aad iska indha ilaa iyo inta doodahaas iyo xaqiijiyo aragtida ah ee tirakoobka (ama, haddii aad doono, experimentally, in taxane ah oo tijaabo). xisaabta noocan oo kale ah had iyo jeer waa soo jiidasho leh. nasiib wacan!