Matematik Ruleet · Caɗeele matematik · hojomaaji 7

Caɗeele: Ko Foti Haa Seero Yalta

Seero ina yalta taarol gooto e nder 37 e hakkundeere. Ko foti fadde goonga, e ko ɗum waɗata fijoowo pari njoɓdi fotndi?

Jaabawol rabbiɗngol

Fadde seero ko jeometrik: hakkundeere taarle 37, medyan 25, fadde gootol e nder noogaas ina ɓura taarle 110. E nder jonnde taarle 200 fijoowo pari njoɓdi fotndi ina fodaa seeroɗi 5,4, ina yiya hakkunde 1 e 10.

fadde hakkundeere
taarle 37
fadde medyan
taarle 25
p(alaa seero e nder taarle 100)
6,5%
seeroɗi e nder taarle 200
5,4 ± 2,3

Caɗeele ɗee

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 → ina jogii porobabilitematematikPorobabiliteSahaa njeñtudi, immorde 0 haa 1 walla 0% haa 100%. Limoore wootere: 1/37 = 2,70%.Tar fof → 1/37 e taarol kala. (a) Hol ko woni porobabilite wonde alaa seero e nder taarle 37 garooje? (b) Hol ko woni fadde medyan? (c) E nder jonnde taarle 200 njoɓdi fotndi, seeroɗi hoto fijoowo foti fodde, e hol ko woni keeri ɗii?

Jaabawol

(a) (36/37)³⁷ = 36,3%. Ko ɓuri tataɓal sahaa, taarle 37 ina mbenna tawa alaa seero fey, ɗum ko hiisa gooto e “hewtude gootol ko famɗi fof e limoore wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof → e nder taarle 37” wonde 63,7% tan. (b) Fadde W ko jeometrik; p(W > k) = (36/37)ᵏ; medyan oo ko k ɗo ɗum ina ƴoŋkoo 0,5, ɗum ko k ≈ 25. Feccere faddeeji ɗii ko taarle 25 walla ko ɓuri famɗude, feccere goɗnde ina ɓuri juutde; hakkundeere 37 ina ɓantee e lappol juutngol. (c) Seeroɗi e nder taarle 200 ko binomial jogiiɗo hakkundeere 200/37 = 5,4 e seerndu ndenndaandumatematikSeerndu ndenndaanduRaasin karee wariyaas; ko woɗɗeende aadanteende njeñtudi e njaru fodaandu.Tar fof → √(200 × (1/37) × (36/37)) ≈ 2,3. Keeri 95% ko hono 1 haa 10.

fadde seeroporobabilite
e nder taarle 1024,0%
e nder taarle 2549,6%
e nder taarle 3763,7%
e nder taarle 5074,6%
e nder taarle 10093,5%
ko ɓuri taarle 110≈ 5%
ko ɓuri taarle 2000,4%
p(W ≤ k) = 1 − (36/37)ᵏ. Hakkundeere 37, medyan 25.

Ko seero ina coggina fijoowo pari njoɓdi fotndi

Seero kala ina coggina pari gooto, seeroɗi ɗii kadi ko ɓural ngal fof e boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof →: e nder taarle 37 hakkundeeje, dañal 18 e majjere 18 ina pottinoo, seero gooto oo ko −1/37. E nder jonnde taarle 200 e $10, seeroɗi 5,4 fodaaɗi ɗii ina coggoo $54, ɗum ko 200 × $10 / 37 tigi. Jonnde jogiinde seeroɗi 2 heɓii baraka $34; jonnde jogiinde seeroɗi 9 heɓii bone $36, ina wayi no ko janfaa. E taabal la partagesariyaLa partageSariya Farayse: so seero yalti, feccere pari njoɓdi fotndi ina ruttee. Ina feccita ɓural kasino e pariiji ɗii haa 1,35%.Tar fof → seero kala ina coggoo feccere pari, limooje ɗee ina pecca e ɗiɗi.

Seeroɗi e nder jonnde taarle 200% jonɗe
0–1
2,5%
2–3
18%
4–5
34%
6–7
28%
8–9
13%
10 walla ko ɓuri
4,5%
% jonɗe
01734%
Binomial(200, 1/37). Fijoowo boɗeere $10 ina yoɓa $10 e seero kala; yaajeende seeroɗi ko yaajeende coggu kiikiiɗe ɗee.

Sariya La partage e RuleetHol Ruleet Internet Ina Janfa? Miijo Juumɗo

Naamnal jokkowal

Hol ko woni porobabilite seeroɗi ɗiɗi jokkondirɗi? (1/37)² = 1/1 369. E kasino ndognoowo taabalji 20 e taarle 50 e waktu, ɗum ko hono seeroɗi ɗiɗi jokkondirɗi gooto nokku woɗɗo e kala waktu 1,4. Fijooɓe yiyɓe ɗum ina mbiya taarorde ndee ko bonnde; hiisa ngal ina wiya ko talaata tan.

Etto ɗum

Simulateer Jonnde Ruleet ina limoo seeroɗi e jonnde kala. Ndogn taarle 100 laabi teemedde seeɗa, natto limoore nde: histogram dow oo ina yalta, e lappol mum juutngol e sara ñaamo. Lappol ngol ko ɗoon daarti ɗii ngaddi.

Formil

p(W > k) = (36/37)ᵏ
E[W] = 37 · medyan ≈ 25
seeroɗi e nder taarle N ~ Binomial(N, 1/37)

Naamne

Mbele seero ina ɓuri yaltude e taarorɗe goɗɗe?

Wonaa e taarorde peewnde. E taarorde ooñiindelaboratuwaarTaarorde ooñiindeTaarorde nde ŋakkeeli mum ɗi fiisik waɗi cuuɗi goɗɗi ina ɓura yaltude 1/37. Ina woowaa, anndetaake si wonaa e taarle ujunaaje winndaaɗe.Tar fof → kala suudukuutorɗeSuuduGootel e cuuɗi 37 limoraaɗi e rotoor. Ina noddee kadi: wenndu, kopp.Tar fof → ina waawi, ina naami kadi taarle ujunaaji ngam anndude ɗum.

Mbele mi foti waɗde sahaa kala jetoŋ e seero hono asurans?

Ko pari 2,70% hono goɗɗi ɗii fof. Ina waylita mbaadi jonnde ndee (seero ina wonta dañal), wonaa coggu ngu.

Ko waɗi medyan oo ina famɗi e hakkundeere ndee?

Sabu senndugol faddeeji ngol ko ooñiingol: faddeeji ɓooyaani keewɗi, seeɗa juutɗi no feewi.

Ƴeewndo weltinoowo

Hakkundeere 37, medyan 25, e lappol juutngol ɗo taalli ɗii ngonata.

Hakkundeere 37, medyan 25, e lappol juutngol ɗo taalli ɗii ngonata.

Iwdi

  1. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, winndannde 3ɓiire, 1968. Majjinde kaalis fijoowo, pecco XIV.
  2. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Pecco 13, ruleet.
ƴeewtaa 2026-09-28misal: ruleet Orop, seero gootolaawol golle ↗iwdi ↗