Problem: komie letan avan zero
Zero sorti enn tour lor 37 an mwayenn. Komie letan ou atann vremem, ek ki sa fer enn zwer ki parye lor peman egal?
Latant pou zero li zeometrik: mwayenn 37 tour, medyann 25, ek enn latant lor ven depas 110 tour. Lor enn sesion 200 tour, enn zwer lor peman egal atann 5.4 zero ek li pou trouv ninport ki ant 1 ek 10.
Problem-la
ZerorouZeroSel kaz ver ki okenn pari peman egal, douzenn ouswa kolonn pa kouver; sours lavantaz kazino. Osi: enn sel zero, 0.Lir tou → ena enn probabilitematematikProbabiliteSans enn rezilta, depi 0 ziska 1 ouswa depi 0% ziska 100%. Enn nimero: 1/37 = 2.70%.Lir tou → 1/37 par tour. (a) Ki probabilite pou pena okenn zero dan 37 tour swivan? (b) Ki latant medyann? (c) Lor enn sesion 200 tour lor peman egal, komie zero enn zwer bizin atann, ek ki interval?
Solision
(a) (36/37)³⁷ = 36.3%. Plis ki enn tier ditan, 37 tour pase san okenn zero, ki mem kalkil ki “omwin enn kout lor enn pari lor enn sel nimeropariPari lor enn sel nimeroEnn sel nimero, peye 35:1.Lir tou → dan 37 tour” ki zis 63.7%. (b) Latant W li zeometrik; p(W > k) = (36/37)ᵏ; medyann-la se k kot sa travers 0.5, vedir k ≈ 25. Mwatie bann latant dire 25 tour ouswa mwins ek mwatie plis; mwayenn 37 la monte akoz long lake-la. (c) Nonb zero dan 200 tour swiv enn lalwa binomial avek mwayenn 200/37 = 5.4 ek ekar-tipmatematikEkar-tipRasinn kare varyans; distans tipik ant enn rezilta ek valer atandi.Lir tou → √(200 × (1/37) × (36/37)) ≈ 2.3. Enn interval 95% se apepre 1 ziska 10.
Komie zero kout enn zwer lor peman egal
Sakenn zero kout enn miz, ek bann zero se tou lavantaz kazino lor rouzpariRouzPari peman egal lor 18 nimero rouz. An franse: rouge.Lir tou →: lor 37 tour mwayenn, 18 gin ek 18 pert anil zot, ek sel zero-la se −1/37 la. Dan enn sesion 200 tour a $10, 5.4 zero atandi kout $54, ki egzakteman 200 × $10 / 37. Enn sesion avek 2 zero inn gagn $34 bonn sans; enn sesion avek 9 zero inn gagn $36 move sans, ek li pou paret triche. Lor enn latab la partagereglemanLa partageRegleman franse: kan zero sorti, ou gagne lamwatie enn miz peman egal. Sa koup lavantaz kazino lor sa bann pari-la an de, ziska 1.35%.Lir tou →, sakenn zero kout mwatie enn miz ek bann sif-la diminie de fwa.
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Kestion swivan
Ki probabilite pou de zero swivan? (1/37)² = 1/1,369. Dan enn kazino ki fer marse 20 latab a 50 tour par er, sa fer apepre enn pe zero dibout-dibout enn kote sak 1.4 er. Bann zwer ki trouv sa dir rou-la kase; kalkil-la dir zis ki zordi enn mardi ordiner.
Esey li
Similater Sesion konte zero par sesion. Lans 100 tour plizir santenn fwa ek trase nonb-la: istogram lao-la pou aparet, avek so long lake adrwat. Se dan sa lake-la ki bann zistwar sorti.
Formil
Kestion
Pa lor enn rou zis. Lor enn rou ki ena defolaboratwarRou ki ena defoEnn rou kot bann defo fizik fer serten kaz pli probab ki 1/37. Rar, ou kapav detekte li zis avek plizier milye tour ki finn note.Lir tou → ninport ki kazekipmanKazEnn bann 37 konpartiman avek nimero lor rotor. Osi: slot, cup.Lir tou → kapav sorti pli souvan, ek bizin plizir milye tour pou trouv sa.
Li enn pari 2.70% kouma tou lezot. Li sanz form sesion-la (enn zero vinn enn gin) me pa so kout.
Akoz distribision bann latant pa simetrik: boukou latant kourt, enn pe latant boukou long.
Enpe riye
Mwayenn 37, medyann 25, ek enn long lake kot bann lezann viv.
Sours
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.