Matematik Ruleet · Miijo aslu · hojomaaji 8

Porobabilite Ruleet

Kala porobabilite ruleet ko limoore cuuɗi peccaande e 37.

Jaabawol rabbiɗngol

p = limooje kuuɓaaɗe / 37. Limoore wootere: 2,70%. Sappo e jeetati: 48,65%. Sahaa jokkondiral ganndaangal ina heɓoo so porobabiliteeji taarol kala fiɓondiraama.

limoore wootere
1/37 · 2,70%
sappo e ɗiɗi
12/37 · 32,43%
njoɓdi fotndi
18/37 · 48,65%
boɗeeje ɗiɗi
23,67%

Taarol gootol

Kala e cuuɗikuutorɗeSuuduGootel e cuuɗi 37 limoraaɗi e rotoor. Ina noddee kadi: wenndu, kopp.Tar fof → 37 ɗii ina foti sahaa, ɗuum waɗi sahaa dañde e ruleet e taarol gootol ko limtugol tan. Pari kuuɓngal limooje nay ina daña 4/37 e kala sahaa, hedde 10,8%. Alaa ko ɓeydotoo e porobabilitematematikPorobabiliteSahaa njeñtudi, immorde 0 haa 1 walla 0% haa 100%. Limoore wootere: 1/37 = 2,70%.Tar fof → taarol gootol, ɗuum ina waɗi fijo ngo fof ina waawi ƴeewteede e kaayit tokoosel.

Porobabilite dañde, e kala pari% taarle
Limoore wootere (1)
2,70%
Limooje ɗiɗi (2)
5,41%
Limooje tati (3)
8,11%
Limooje nay (4)
10,81%
Limooje jeegom (6)
16,22%
Sappo e ɗiɗi / kolon (12)
32,43%
Njoɓdi fotndi (18)
48,65%
% taarle
024,3248,65%
Kala pari ko limooje kuuɓaaɗe peccaaɗe e 37. Njoɓdi ina ustoo nde kuuɓal ɓeydotoo, ngam njaru fodaandu wona −2,70% gootu ndun e kala daaɗol.

Taarle keewɗe

Taarle ina ceertii, ɗuum waɗi porobabiliteeji jokkondiral ina fiɓondira. BoɗeejepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof → ɗiɗi jokkondirɗe: (18/37)² = 23,7%. Boɗeere caggal ɗuum seerotaarordeSeeroSuudu haako wootere nde hay pari njoɓdi fotndi, sappo e ɗiɗi walla kolon kuuɓataa; ko ɗum woni iwdi ɓural kasino. Ina noddee kadi: seero gooto, 0.Tar fof →: (18/37)(1/37) = 1,3%. Sappo e jeeɗiɗi laabi ɗiɗi jokkondirɗi: (1/37)² = 0,073%, hedde gooto e nder 1 369. Doggol ina jogii maanaa e jokkondiral ganndaangal, alaa e limtugol: “boɗeere caggal ɗuum ɓaleerepariƁaleerePari njoɓdi fotndi e limooje 18 ɓaleeje. E Farayse: noir.Tar fof →” ko 25,0% kono “boɗeere wootere e ɓaleere wootere e taarle ɗiɗi, doggol fof” ko 50,0%.

Taarle Ruleet Ceertuɗe

Hay laawol gootol

Huutoro ko heddii. Sahaa alaa hay dañal gootal e limoore wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof → e taarle 37 ko (36/37)³⁷ = 36,3%, ɗuum waɗi sahaa dañde hay laawol gootol ko 63,7%, wonaa “goongaaji” ɗi fijooɓe heewɓe ndiiwata e sahaaji 37 ɗi 1 e nder 37. Limtol gootol ngol ina hollira limoore ina jogii sahaa hedde 1 e nder 3 wonde hay huunde ummataa e taarle 37, ɗuum waɗi tabalo njeñtuɗi ina hollira kala sahaa limooje seeɗa “jaangunde”.

taarlep(alaa dañal, limoore wootere)p(dañal hay gootal)
1076,0%24,0%
3736,3%63,7%
7413,2%86,8%
1006,5%93,5%
1501,7%98,3%
2000,4%99,6%
(36/37)ⁿ e 1 − (36/37)ⁿ. Hay caggal taarle 100, limoore wootere e nder sappo e joy ummaaki tawo.

Njeñtuɗi Ruleet: Tarugol Tabalo

Sahaa fodaaɗo ngam habbaade

E hakkundeere limoore wootere ina ummoo laawol gootol e kala taarle 37, kono habbaade ina waylii no feewi: medyan habbaade ko hedde taarle 25 (feccere sahaaji ina arda ɗum) e habbaade wootere e nder noogas ina ɓura taarle 110. Sahaaji habbaade e kuugal jeometrik ina njuuti law, kadi fijoowo “anndungo” wonde limoore ina hewtii caggal taarle 60 ina sifoo huunde nde waɗata laawol gootol e nder joy.

Miijo Juumɗo: Limooje “Haanii Yaltude”

Juumeeji heewɗi

Ɓeydude porobabiliteeji huuɗe waawuɗe waɗde kamɓe ɗiɗo fof (boɗeere walla peccotaake wonaa 36/37; ko 26/37, sabu limooje sappo ko ɗiɗi ɗii fof). Fiɓondirde huuɗe e taarol gootol (boɗeere e peccotaake e taarol gootol ko 10/37, wonaa 18/37 × 18/37). Hiisaade taarle ɓennuɗe wonde ko e jokkondiral ngal pari maa woni: caggal boɗeeje sappo, sahaa boɗeere sappo e gooto ko 18/37, wonaa (18/37)¹¹.

Ko honɗum woni kot e ruleet, ko honno ngo ceertiri e porobabilite?

Kasinooji ina mbiya njoɓdikaalisNjoɓdiKo pari dañndi ruttata, wiyaa “X e 1” ɓeydaa e pari ruttaaɗo.Tar fof → hono kot. Limoore wootere ina daña e porobabilite 1/37, ɗuum waɗi kot dañde e ruleet e limoore wootere ko 36 e 1 e dow maa. Njoɓdi 35 e 1 ina ustoo initekaalisInitePari fuɗɗoode mo sistem walla fijoowo gollirta. Jokkondirɗe pari ina cifee e initeeji ngam ɗi kuutoroo e kala taabal.Tar fof → gootal, ɗum woni ɓural kasinomatematikƁural kasinoGeɗal kala pari ngal kasino jogiiyata e hakkundeere: 2,70% e ruleet Orop.Tar fof → e mbaadi mum aranndi. Waylugol: kot e dow maa = (1 − p)/p; porobabilite = 1/(kot + 1).

Formil

p(pari) = n / 37
p(A caggal ɗuum B) = p(A) · p(B)
p(hay laawol gootol e k) = 1 − (1 − p)ᵏ
kot e dow maa = (1 − p) / p

Naamne

Ko honɗum woni porobabilite seero laabi ɗiɗi jokkondirɗi?

(1/37)² = 1/1369 ≈ 0,073%.

Ko honɗum woni sahaa boɗeere walla ɓaleere?

36/37 = 97,3%. Seero ko ko heddii.

Mbele 17 ko limoore ɓurnde ummaade?

Ɗe 37 ɗee fof ko 1/37. Sappo e jeeɗiɗi ko limoore ɓurnde heɓde pariiji, ɗum ko huunde nde yowitii e yimɓe.

Weltaare e Matematik

Etu ɗum hoore maa adii. Kala jaabawol ina suuɗii; uddit ɗum so a heblii.

  1. A waɗa pari e boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof →, taarol e taarol. Hol porobabilite nde dañal maa joyaɓal arata e taarol jeetataɓol tigi? E nde a heɓata dañe joy e nder taarle jeetati adiiɗe ɗee?

    Hollu jaabawol ngol

    Jaabawol 12,9%, hono 1 e nder 8, ngam dañal joyaɓal e taarol jeetataɓol. 33,4% ngam dañe joy haa ɗoon.

    Dañal joyaɓal e taarol jeetataɓol ina firta huunde ɗiɗi: taarol jeetataɓol ina daña, taarle jeeɗiɗi adiiɗe ɗee ina njogii dañe nay tigi e majjeeje tati, e kala doggol. Ina woodi laabi 35 ngam waɗde dañe nay e nder taarle jeeɗiɗi.

    Ɗum waɗi porobabilite ndee ko 35 × (18/37)⁵ × (19/37)³ = 35 × 0,02725 × 0,1354 = 12,9%.

    Ngam dañe joy haa taarol jeetataɓol, ɓeydu terme gootum ngam dañal joyaɓal e taarle joyaɓe, jeegomaɓe e jeeɗiɗaɓe: 2,7% + 7,0% + 10,8% + 12,9% = 33,4%. Ganndiiɓe statistik ina noddira ɗum senndugol binomiyal ñiddungal: etaaɗe njelu limoore dañe tabitinaande naamnotoo. Taylor (2021) ina limta naamnal gootal ngal e taarorde Amerik, 12,2%.

Ƴeewndo weltinoowo

Limto cuuɗi. Pecc e 37. Fiɓondir ngam jokkondiral. Gasii.

Limto cuuɗi. Pecc e 37. Fiɓondir ngam jokkondiral. Gasii.

Iwdi

  1. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, muulnugol 3, 1968. Gambler’s ruin, pecce XIV.
  2. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Pecce 13, ruleet.
  3. Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021.
ƴeewtaa 2026-09-28misal: ruleet Orop, seero gootolaawol golle ↗iwdi ↗