Xisaabta Roulette · Masalo xisaabeed · 7 daqiiqo

Masalo: Intee Ka Hor Eberka

Q: Eberku ma ka suurtagal badan yahay giraangirada qaar?

Ma aha mid caddaalad ah. Giraangir eex leh god kasta wuu noqon karaa, waxayna qaadan lahayd kumanaan wareeg in la ogaado.

Eberku wuxuu ku dhacaa hal wareeg 37 kiiba celcelis ahaan. Intee ayaad dhab ahaan sugtaa, maxayse taasi ku samaysaa sharadle lacag isle'eg ah?

Jawaab gaaban

Sugitaanka eberku waa joometri: celcelis 37 wareeg, dhexdhexaad 25, hal sugitaan labaatankii kiibana wuxuu ka badan yahay 110 wareeg. Fadhi 200 wareeg ah, sharadle lacag isle'eg ah wuxuu filayaa 5.4 eber wuxuuna arki doonaa meel kasta oo u dhexeysa 1 ilaa 10.

celceliska sugitaanka

37 wareeg

sugitaanka dhexdhexaadka ah

25 wareeg

p(eber la'aan 100 wareeg)

6.5%

eberrada 200 wareeg

5.4 ± 2.3

Masalada

EberkugiraangirEberHal godka cagaaran ee aan daboolin sharad lacag isle'eg ah, dersin ama tiir; isha faa'iidada kasiinada. Sidoo kale: single zero, 0.Akhri dhammaan → wuxuu leeyahay itimaalxisaabItimaalFursadda natiijo, 0 ilaa 1 ama 0% ilaa 100%. Hal lambar: 1/37 = 2.70%.Akhri dhammaan → 1/37 wareeggii. (a) Waa maxay itimaalka eber la'aanta 37-ka wareeg ee soo socda? (b) Waa maxay sugitaanka dhexdhexaadka ah? (c) Fadhi 200 wareeg ah oo lacag isle'eg ah, imisa eber ayuu ciyaartoygu filan karaa, baaxaddu waa maxay?

Xalal

(a) (36/37)³⁷ = 36.3%. In ka badan saddex meelood meel waqtiga, 37 wareeg ayaa dhaafa iyadoo eber gabi ahaanba aan soo bixin, taasoo ah isla xisaabta “ugu yaraan hal ku dhac hal lambarsharadHal lambarHal lambar oo keliya, wuxuu bixiyaa 35:1.Akhri dhammaan → 37 wareeg gudahood” oo ah kaliya 63.7%. (b) Sugitaanka W waa joometri; p(W > k) = (36/37)ᵏ; dhexdhexaadku waa k-da ay tani ka gudubto 0.5, taasoo ah k ≈ 25. Kala bar sugitaannada waa 25 wareeg ama ka gaaban, kala barka kalena ka dheer; celceliska 37 waxaa kor u jiida dabada dheer. (c) Eberrada 200 wareeg waa binomial oo celceliskoodu yahay 200/37 = 5.4, leexashada caadiga ahnaxisaabLeexashada caadiga ahXididka labajibbaarka ee kala-duwanaanshaha; masaafada caadiga ah ee natiijo ay u jirto qiimaha la filayo.Akhri dhammaan → √(200 × (1/37) × (36/37)) ≈ 2.3. Baaxad 95% ah waa qiyaastii 1 ilaa 10.

sugitaanka eberkaitimaal

10 wareeg gudahood24.0%

25 wareeg gudahood49.6%

37 wareeg gudahood63.7%

50 wareeg gudahood74.6%

100 wareeg gudahood93.5%

in ka badan 110 wareeg≈ 5%

in ka badan 200 wareeg0.4%

p(W ≤ k) = 1 − (36/37)ᵏ. Celcelis 37, dhexdhexaad 25.

Waxa eberku ku kacayo sharadle lacag isle'eg ah

Eber kastaa wuxuu ku kacaa hal sharad, eberradu waa faa'iidada kasiinada oo dhan ee casaankasharadCasaanSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee casaanka ah. Faransiis: rouge.Akhri dhammaan →: 37 wareeg oo celcelis ah, 18-ka guul iyo 18-ka khasaare way is baabi'iyaan, eberka keliya ayaa ah −1/37. Fadhi 200 wareeg ah oo $10 ah, 5.4-ta eber ee la filayo waxay ku kacaan $54, taasoo si sax ah u ah 200 × $10 / 37. Fadhi 2 eber leh wuxuu helay $34 nasiib wanaagsan; fadhi 9 eber leh wuxuu helay $36 nasiib xun, wuxuuna u ekaan doonaa mid la khiyaanay. Miis la partagexeerLa partageXeer Faransiis ah: marka eberku soo baxo, kala badh sharad lacag isle'eg ah ayaa la soo celiyaa. Wuxuu faa'iidada kasiinada sharadyadaas u dhimaa 1.35%.Akhri dhammaan → ah eber kastaa wuxuu ku kacaa nus sharad, tirooyinkuna way kala bar noqdaan.

Eberrada fadhi 200 wareeg ah% fadhiyada

0–1

2.5%

2–3

18%

4–5

34%

6–7

28%

8–9

13%

10 ama ka badan

4.5%

% fadhiyada

01734%

Binomial(200, 1/37). Sharadlaha casaanka $10 wuxuu bixiyaa $10 eber kasta; kala-fidsanaanta eberradu waa kala-fidsanaanta qiimaha habeenka.

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Su'aasha xigta

Waa maxay itimaalka laba eber oo isku xiga? (1/37)² = 1/1,369. Kasiino socodsiisa 20 miis oo 50 wareeg saacaddii ah, taasi waa qiyaastii hal lammaane eber oo isdaba joog ah meel uun 1.4-tii saacadoodba. Ciyaartoyda arka waxay go'aamiyaan in giraangirtu jabtay; xisaabtu waxay leedahay waa Talaado caadi ah.

Isku day

Jilaaga Fadhiga Roulette wuxuu tiriyaa eberrada fadhi kasta. Socodsii 100 wareeg dhowr boqol oo jeer oo sawir tirada: histogram-ka kore ayaa soo muuqan doona, isagoo leh dabadiisa dheer ee midig. Dabada ayay sheekooyinku ka yimaadaan.

Qaacido

p(W > k) = (36/37)ᵏ

E[W] = 37 · dhexdhexaad ≈ 25

eberrada N wareeg ~ Binomial(N, 1/37)

Su'aalo

Eberku ma ka suurtagal badan yahay giraangirada qaar?

Ma aha mid caddaalad ah. Giraangir eex lehshaybaarGiraangir eex lehGiraangir ay cilladaheeda jireed ka dhigaan godad qaarkood kuwo ka itimaal badan 1/37. Waa dhif, waxaana lagu ogaan karaa oo keliya kumanaan wareeg oo la diiwaangeliyay.Akhri dhammaan → godqalabGodMid ka mid ah 37-ka qol ee lambarrada leh ee rotor-ka. Sidoo kale: slot, cup.Akhri dhammaan → kasta wuu noqon karaa, waxayna qaadan lahayd kumanaan wareeg in la ogaado.

Ma inaan had iyo jeer chip dul dhigaa eberka caymis ahaan?

Waa sharad 2.70% ah sida mid kasta oo kale. Wuxuu beddelaa qaabka fadhiga (eber wuxuu noqdaa guul), ma beddelo qiimaha.

Maxaa dhexdhexaadku uga yar yahay celceliska?

Sababtoo ah qaybinta sugitaannadu way leexsan tahay: sugitaanno gaagaaban oo badan, qaar yar oo aad u dhaadheer.

Kaftan yar

$Celcelis 37, dhexdhexaad 25, iyo dabo dheer oo halyeeyadu ku nool yihiin.$

Celcelis 37, dhexdhexaad 25, iyo dabo dheer oo halyeeyadu ku nool yihiin.

Ilaha

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, daabacaadda 3aad, 1968. Burburka khamaarlaha, cutubka XIV.
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Cutubka 13, roulette.

la eegay 2026-09-28model: Yurub, hal eberhabka shaqada ↗ilaha ↗