Prɔblɛm: di bɔtde wil
Ɔmɔs spin bifo wan nɔmba kam bak? Smɔl pas aw bɔku pipul de gɛs.
Di bɔtde prɔblɛm pan wil wit 37 pɔkitikwipmɛntPɔkitWan pan di 37 smɔl ples dɛn wit nɔmba pan di rotɔ. Dɛn kin kɔl am bak: slot, kɔp.Rid ɔl →: afta jɔs 8 spin, di chans pas af se wan nɔmba dɔn kam tu tɛm. Pleya dɛn de rid nɔmba we kam bak as patɛn; bɔt na so fɛr wil fɔ biev.
Di prɔblɛm
Spin fɛr Yuropian wil. Ɔmɔs spin te di prɔbabilitimatematiksPrɔbabilitiDi chans fɔ wan rizɔlt, frɔm 0 to 1 ɔ frɔm 0% to 100%. Wan nɔmba: 1/37 = 2.70%.Rid ɔl → se tu spin dɔn sho di sem nɔmba go pas af? Bɔku pleya de gɛs sɔmwe nia 18 ɔ 19, af pan 37. Di ansa na 8.
Di ansa
Kalkul di prɔbabiliti se no nɔmba nɔ kam bak, ɛn pul am frɔm wan. Afta k spin, p(ɔl difrɛn) = (37/37)(36/37)(35/37)…((38 − k)/37). Fɔ k = 8: 1 × 0.973 × 0.946 × 0.919 × 0.892 × 0.865 × 0.838 × 0.811 ≈ 0.44, so p(wan kam bak) ≈ 0.56. Fɔ k = 14 i na 0.93; fɔ k = 20 i na 0.996. Wi fil rɔng bikɔs di nɔmba fɔ pe spin de gro lɛk k², ɛn ɛni pe kin mach.
Wetin mek i impɔtant na di tebul
Rizɔlt bɔd we sho di las 20 nɔmba go nia ɔltɛm sho wan nɔmba we kam bak, bɔku tɛm tu ɔ tri. Pleya dɛn de si “17 kam tu tɛm insay tɛn spin” ɛn dɛn de se 17 ɔt; di bɔtde kalkuleshɔn se nɔmba we kam bak insay tɛn spin de apin 74% pan di tɛm, ɛn di nɔmba we kam bak na ɛni kayn wan. Di patɛn de fɔ tru; di minin nɔ de.
Di prɔblɛm we de kam afta
Ɔmɔs spin te wan patikyula nɔmba, lɛk 17, dɔn kam tu tɛm? Dat na difrɛn kwɛstyɔn wit ansa we big pas bɔku: di wet we fɔ ɛkspɛkt na 74 spin, ɛn di prɔbabiliti fɔ tu 17 insay 20 spin na lɛk 10%. Di difrɛns bitwin “wan nɔmba kam bak” (8 spin) ɛn “dis nɔmba kam bak” (74 spin) na di ol difrɛns bitwin patɛn we yu si afta ɛn prɛdikshɔn we yu mek bifo.
Tray am
Ple di Tray gem fɔ tɛn spin ɛn luk di wetin dɔn apin. Bɔku tɛm wan nɔmba go kam bak. Ple am bak. Di nɔmba we kam bak go difrɛn. Du dis tɛn tɛm ɛn yu dɔn si di bɔtde prɔblɛmmatematiksBɔtde prɔblɛmƆmɔs pipul yu nid bifo tu pan dɛn go pɔsibul gɛt di sem bɔtde, ɔ ɔmɔs spin bifo wan nɔmba go pɔsibul kam bak. Pan wil wit 37 pɔkit, 8 spin dɔn du fɔ gɛt chans we pas af.Rid ɔl →; du am wan tawzin tɛm (di simulɛta dɛn kin du am) ɛn yu dɔn mɛzhɔ am.
Fɔmula
Kwɛstyɔn dɛn
Ɛgzaktli, wit 37 pɔkit instɛd fɔ 365 dez. 23 pipul de gi 50% fɔ bɔtde; 8 spin de gi 56% fɔ di wil.
50% afta lɛk 19 spin. Stil nɔmal tin.
Nɔ. Tawzin tawzin spin frɔm wan wil go sho am; wan nɔmba we kam bak nɔ de ɛva sho am.
Ple wit Mat
Tray dɛn yusɛf fɔs. Ɛni ansa de ayd; opin am we yu rɛdi.
Rizɔlt bɔd nia Amɛrikan wil de sho di las 16 spin. Ɔmɔs chans de se nɔ nɔmba nɔ kam tu tɛm pan am?
Sho di ansa
Ansa Lɛk 2.5%: lɛk 39 bɔd pan 40 de sho atlis wan nɔmba we kam bak.
Go spin bay spin. Di fɔs spin fit bi ɛnitin. Di sɛkɔn wan fɔ mis am: 37 chans pan 38. Di tɔd wan fɔ mis dɛn tu: 36 pan 38. Di sikstin spin fɔ mis fiftin nɔmba: 23 pan 38.
Mɔltiplay: 38/38 × 37/38 × 36/38 × … × 23/38 ≈ 0.0246.
Bɔd we nɔ gɛt nɔmba we kam bak na di rɛr wan. Bɔd we gɛt nɔmba we kam bak nɔ de tɔk natin bɔt di wil.
Pan tɛn spin fɔ Yuropian wil, wetin na di chans se 17 go kam ɛgzakt fayv tɛm? Se sɔm nɔmba, ɛni nɔmba, go kam fayv tɛm ɔ mɔ? Ɛn se sɔm nɔmba go kam atlis tri tɛm pan fɔ spin?
Sho di ansa
Ansa 17 ɛgzakt fayv tɛm: 1 pan 315,576. Sɔm nɔmba fayv tɛm ɔ mɔ: lɛk 1 pan 8,333. Sɔm nɔmba tri tɛm ɔ mɔ pan fɔ spin: 1 pan 349.
17 fayv tɛm: pik wish fayv pan di tɛn spin, 252 we, ɛni wan wit chans (1/37)⁵ × (36/37)⁵. Togɛda, 1 pan 315,576.
Sɔm nɔmba: ɛni wan pan di 37 nɔmba gɛt chans fɔ 1 pan 308,325 fɔ kam fayv tɛm ɔ mɔ, ɛn dat de gi 37 pan 308,325, ɔ 1 pan 8,333. Di rɛr kes we tu nɔmba kam fayv tɛm ɛni wan, wi kɔnt am tu tɛm, bɔt if wi pul am, natin nɔ chenj na dis lɛvul.
Tri tɛm pan fɔ spin: fɔ wan nɔmba, 4 × 36 + 1 = 145 pan di 37⁴ rizɔlt we fit kam; fɔ ɛni wan pan di 37 nɔmba, 145/37³ = 1 pan 349.
Fɔ wil wit dɔbul zirowilZiroDi wan grin pɔkit we nɔ ivin-mɔni, dɔzin ɔ kɔlɔm bɛt nɔ kɔba; na usay di kasino advantej kɔmɔt. Dɛn kin kɔl am bak: wan ziro, 0.Rid ɔl →, di sem nɔmba dɛn na 1 pan 359,275, 1 pan 9,243 ɛn 1 pan 368. Di difrɛns bitwin “17” ɛn “sɔm nɔmba” na di bɔtde prɔblɛmmatematiksBɔtde prɔblɛmƆmɔs pipul yu nid bifo tu pan dɛn go pɔsibul gɛt di sem bɔtde, ɔ ɔmɔs spin bifo wan nɔmba go pɔsibul kam bak. Pan wil wit 37 pɔkit, 8 spin dɔn du fɔ gɛt chans we pas af.Rid ɔl → bak: na 37 we de fɔ sɔprayz yu.
Smɔl jok fɔ ɛz di maynd
Sɔntin de kam bak ali. Dat sɔntin na ɛni kayn wan.
Usay wi gɛt am frɔm
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Wizard of Odds. “Ask the Wizard”, kwɛstyɔn bɔt rulɛt.