Ikibazo: Uruziga rw'Isabukuru
Ni amazunguruka angahe mbere y'uko umubare runaka wisubiramo? Ni make cyane kurusha uko abantu benshi bakeka.
Ikibazo cy'isabukuru ku ruziga rw'utuzuibikoreshoAkazuKamwe mu tuzu 37 twanditseho imibare turi kuri rotor. Nanone: slot, cup.Soma byose → 37: nyuma y'amazunguruka 8 gusa, amahirwe ko umubare runaka umaze gusohoka kabiri arenga kimwe cya kabiri. Abakinnyi bafata gusubiramo nk'imiterere runaka; nyamara ni imyitwarire iteganyijwe y'uruziga rutabogamye.
Ikibazo
Zengurutsa uruziga rw'i Burayi rutabogamye. Ni amazunguruka angahe kugeza igihe amahirweimibareAmahirweAmahirwe y'igisubizo, kuva kuri 0 kugeza kuri 1 cyangwa kuva kuri 0% kugeza kuri 100%. Umubare umwe: 1/37 = 2,70%.Soma byose → y'uko nibura amazunguruka abiri yerekanye umubare umwe arenga kimwe cya kabiri? Abakinnyi benshi bakeka hafi 18 cyangwa 19, kimwe cya kabiri cya 37. Igisubizo ni 8.
Igisubizo
Bara amahirwe y'uko nta gusubiramo kubaho maze uyakure kuri rimwe. Nyuma y'amazunguruka k, p(yose atandukanye) = (37/37)(36/37)(35/37)…((38 − k)/37). Kuri k = 8: 1 × 0,973 × 0,946 × 0,919 × 0,892 × 0,865 × 0,838 × 0,811 ≈ 0,44, bityo p(gusubiramo runaka) ≈ 0,56. Kuri k = 14 ni 0,93; kuri k = 20 ni 0,996. Ibyo umuntu yibwira bipfa kuko umubare w'impea z'amazunguruka ukura nka k², kandi impea iyo ari yo yose ishobora guhura.
Impamvu bifite akamaro ku meza
Ikibaho cy'ibisubizo cy'imibare 20 iheruka hafi buri gihe kizerekana nibura gusubiramo kumwe, akenshi kabiri cyangwa gatatu. Abakinnyi babona “17 yasohotse kabiri mu mazunguruka icumi” bakanzura ko 17 ishyushye; imibare y'isabukuru ivuga ko gusubiramo mu mazunguruka icumi kubaho 74% by'igihe kandi umubare wisubiyemo uba watunguranye. Imiterere irahari koko; igisobanuro cyo ntikiriho.
Ikibazo gikurikiraho
Ni amazunguruka angahe kugeza igihe umubare runaka wihariye, urugero 17, usohotse kabiri? Icyo ni ikibazo gitandukanye gifite igisubizo kinini cyane: igihe giteganyijwe cyo gutegereza ni amazunguruka 74, kandi amahirwe ya 17 ebyiri mu mazunguruka 20 ni hafi 10%. Itandukaniro riri hagati ya “umubare runaka wisubiramo” (amazunguruka 8) na “uyu mubare wisubiramo” (amazunguruka 74) ni ryo tandukaniro ryose riri hagati y'imiterere ubona nyuma n'iteganya ukora mbere.
Gerageza
Kina Umukino w'Igerageza amazunguruka icumi maze urebe amateka. Ubusanzwe hazaba harimo gusubiramo. Ongera ukine. Umubare wisubiyemo uzaba utandukanye. Bikore incuro icumi maze uzaba wabonye ikibazo cy'isabukuruimibareIkibazo cy'isabukuruUmubare w'abantu ukenewe kugira ngo babiri bashobora kuba bafite isabukuru imwe, cyangwa umubare w'amazunguruka ukenewe kugira ngo umubare ushobora kugaruka. Ku ruziga rw'utuzu 37, amazunguruka 8 arahagije ngo amahirwe arenge kimwe cya kabiri.Soma byose →; bikore incuro igihumbi (amagerageza abishobora) maze uzaba wagipimye.
Formula
Ibibazo
Ni kimwe neza, ariko n'utuzu 37 aho kuba iminsi 365. Abantu 23 batanga 50% ku masabukuru; amazunguruka 8 atanga 56% ku ruziga.
50% nyuma y'amazunguruka hafi 19. Biracyari ibisanzwe.
Oya. Ibihumbi by'amazunguruka y'uruziga rumwe ni byo byabigaragaza; gusubiramo ntibyigera bibigaragaza.
Kwishimisha n'Imibare
Banza ubigerageze ubwawe. Buri gisubizo kirapfunyitse; ugifungure igihe witeguye.
Ikibaho cy'ibisubizo kiri iruhande rw'uruziga rw'Abanyamerika cyerekana amazunguruka 16 aheruka. Ni ayahe mahirwe y'uko nta mubare ugaragaraho kabiri?
Erekana igisubizo
Igisubizo Hafi 2,5%: hafi ibibaho 39 muri 40 byerekana nibura umubare umwe wisubiyemo.
Genda izunguruka ku rindi. Izunguruka rya mbere rishobora kuba icyo ari cyo cyose. Irya kabiri rigomba kudahura na ryo: amahirwe 37 muri 38. Irya gatatu rigomba kudahura n'ayo yombi: 36 muri 38. Irya cumi na gatandatu rigomba kudahura n'imibare cumi n'itanu: 23 muri 38.
Kuba: 38/38 × 37/38 × 36/38 × … × 23/38 ≈ 0,0246.
Ikibaho kidafite umubare wisubiyemo ni cyo kiboneka gake. Ikibaho gifite umubare wisubiyemo nta cyo kivuga ku ruziga.
Mu mazunguruka icumi y'uruziga rw'i Burayi, ni ayahe mahirwe y'uko 17 iza inshuro eshanu neza? Y'uko umubare runaka, uwo ari wo wose, uza inshuro eshanu cyangwa zirenga? Kandi y'uko umubare runaka uza nibura inshuro eshatu mu mazunguruka ane?
Erekana igisubizo
Igisubizo 17 inshuro eshanu neza: 1 kuri 315.576. Umubare runaka inshuro eshanu cyangwa zirenga: hafi 1 kuri 8.333. Umubare runaka inshuro eshatu cyangwa zirenga mu mazunguruka ane: 1 kuri 349.
17 inshuro eshanu: hitamo amazunguruka atanu muri icumi, uburyo 252, buri bumwe bufite amahirwe ya (1/37)⁵ × (36/37)⁵. Byose hamwe, 1 kuri 315.576.
Umubare runaka: buri mubare muri 37 ufite amahirwe ya 1 kuri 308.325 yo kuza inshuro eshanu cyangwa zirenga, bitanga 37 kuri 308.325, cyangwa 1 kuri 8.333. Ikibazo kidakunze kubaho cy'imibare ibiri iza inshuro eshanu buri umwe kibarwa kabiri, ariko kugikuramo nta cyo bihindura kuri uru rugero rw'ubusobanuro.
Inshuro eshatu mu mazunguruka ane: ku mubare umwe, 4 × 36 + 1 = 145 mu bisubizo 37⁴ bishoboka; ku mubare uwo ari wo wose muri 37, 145/37³ = 1 kuri 349.
Ku ruziga rwa zeruuruzigaZeruAkazu kamwe k'icyatsi katafatwa n'itega ryishyura kimwe ku kindi, irya dazeni cyangwa iry'inkingi; ni ho inyungu ya kazino ikomoka. Nanone: zeru imwe, 0.Soma byose → ebyiri, imibare ihuye ni 1 kuri 359.275, 1 kuri 9.243 na 1 kuri 368. Itandukaniro hagati ya “17” n'“umubare runaka” ni ikibazo cy'isabukuruimibareIkibazo cy'isabukuruUmubare w'abantu ukenewe kugira ngo babiri bashobora kuba bafite isabukuru imwe, cyangwa umubare w'amazunguruka ukenewe kugira ngo umubare ushobora kugaruka. Ku ruziga rw'utuzu 37, amazunguruka 8 arahagije ngo amahirwe arenge kimwe cya kabiri.Soma byose → na none: hari uburyo 37 bwo gutungurwa.
Akanya k'urwenya
Hari ikintu cyisubiramo hakiri kare. Icyo kintu kiba cyatunguranye.
Inkomoko
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Wizard of Odds. “Ask the Wizard”, ibibazo bya roulette.