Taprubabilit deg rulit
Yal taprubabilit n rulit d amḍan n texxamin yebḍan ɣef 37.
p = uṭṭunen yettwaṭṭfen / 37. Yiwen wuṭṭun: 2,70%. Tmenṭac: 48,65%. I wazrar n yigmaḍ yettwasbadun, tiprubabiliyin n yal tuzzya ttwasgutent.
Tuzzyiwin yiwet yiwet
Yal yiwet seg 37 n texxaminibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk → tesɛa yiwet n taprubabilit, ihi taprubabilit n rrbeḥ deg rulit deg yiwet n tuzzya d leḥsab kan. Rrehn ɣef ukkuẓ n wuṭṭunen yettarbaḥ 4/37 n wakud, qrib 10,8%. Ulac ayen nniḍen deg taprubabilittusnaktTaprubabilitAzal n yiwen ugmuḍ ad d-yeḍru, seg 0 ɣer 1 neɣ seg 0% ɣer 100%. Yiwen wuṭṭun: 1/37 = 2,70%.Ɣer akk → n yiwet n tuzzya, d ayɣer urar akk yezmer ad yettwasleḍ ɣef tcerwiḍt n lkaɣeḍ.
Aṭas n tuzzyiwin
Tuzzyiwin d timanayin, ihi tiprubabiliyin n wazrar n yigmaḍ ttwasgutent. Sin n uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → yeṭṭafaren: (18/37)² = 23,7%. Azeggaɣ sakin ilemaḍebsiIlemTaxxamt tazegzawt tasuft ur yeṭṭif ula d yiwen n rrehn s lexlaṣ imsawi, n ddzina neɣ n tgejdit; d aɣbalu n lmaziyya n lkazinu. Daɣen: yiwen yilem, 0.Ɣer akk →: (18/37)(1/37) = 1,3%. Sbeɛṭac snat n tikkal yeṭṭafaren: (1/37)² = 0,073%, qrib yiwet seg 1 369. Amyizwer yesɛa azal i wazrar yettwasbadun, mačči i umḍan: «azeggaɣ sakin aberkanrrehnAberkanRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen iberkanen. S tefransist: noir.Ɣer akk →» d 25,0%, maca «yiwen uzeggaɣ d yiwen uberkan deg snat n tuzzyiwin, s yal amyizwer» d 50,0%.
Ma drus yiwet n tikkelt
Sseqdcet ayen yettwakemmalen. Taprubabilit ur yeṭṭif ara yiwen wuṭṭunrrehnYiwen wuṭṭunYiwen wuṭṭun kan, ixelleṣ 35:1.Ɣer akk → deg 37 n tuzzyiwin d (36/37)³⁷ = 36,3%, ihi taprubabilit n yiwet n tuṭṭfa ma drus d 63,7%, mačči d «ayen yettwaḍmen» i ttraǧun aṭas n yimuraren seg 37 n tegniwin s 1 seg 37. Yiwen leḥsab yeqqar belli uṭṭun yesɛa qrib 1 seg 3 n taprubabilit ur d-yettban ara akk deg 37 n tuzzyiwin, d ayɣer tafelwit n yigmaḍ tesskanay yal tikkelt kra n wuṭṭunen «isemmaḍen».
Akud n uraǧu yettwaṛǧan
S ulemmas yiwen wuṭṭun yettban-d yiwet n tikkelt yal 37 n tuzzyiwin, maca araǧu yettbeddil aṭas: azal n tlemmast n uraǧu qrib 25 n tuzzyiwin (azgen n wakud yettas-d zik) yerna yiwen uraǧu seg ɛecrin yezgar 110 n tuzzyiwin. Akud n uraǧu n ukala ajyumitran yesɛa ajeḥnuḍ aɣezfan, yerna amurar i «yessnen» belli uṭṭun yewweḍ-d wakud-is deffir 60 n tuzzyiwin yettglam ayen yeḍrun yiwet n tikkelt seg semmus.
Tuccḍiwin yettwafen s waṭas
Timernit n tiprubabiliyin i yineḍruyen i yezmren ad ḍrun s sin (azeggaɣ neɣ aryan mačči d 36/37; d 26/37, acku mraw n wuṭṭunen d sin yid-sen). Asgut i yineḍruyen deg yiwet n tuzzya (azeggaɣ d uryan deg yiwet n tuzzya d 10/37, mačči 18/37 × 18/37). Aḥsab n tuzzyiwin yezrin am wakken d aḥric n wazrar i ɣef tettrehnem tura: deffir mraw n uzeggaɣ, taprubabilit n wis ḥdac d 18/37, mačči (18/37)¹¹.
D acu i d assaɣ n lexlaṣ deg rulit, d wamek i yemgarad ɣef taprubabilit?
Lkazinu ttinint lexlaṣidrimenLexlaṣAyen i d-yettak rrehn i yerbḥen, yettwanna «X ɣef 1» nnig rrehn i d-yettuɣalen.Ɣer akk → s wassaɣ. Yiwen wuṭṭun yettarbaḥ s taprubabilit n 1/37, ihi assaɣ n rrbeḥ deg rulit ɣef yiwen wuṭṭun d 36 ɣef 1 mgal. Lexlaṣ n 35 ɣef 1 ixuṣṣ-it yiwen uferdisidrimenAferdisRrehn agejdan s wacu i yettxeddem unagraw neɣ amurar. Inagrawen n usnerni ttwaglamen s yiferdisen akken ad ilin i yal ṭṭabla.Ɣer akk →, d wagi i d lmaziyya n lkazinutusnaktLmaziyya n lkazinuAḥric n yal rrehn i teṭṭef lkazinu s ulemmas: 2,70% deg rulit tawrupit.Ɣer akk → deg talɣa-s tamezwarut. Abeddel: assaɣ mgal = (1 − p)/p; taprubabilit = 1/(assaɣ + 1).
Tasemselt
Isteqsiyen
(1/37)² = 1/1369 ≈ 0,073%.
36/37 = 97,3%. Ilem d ayen d-yeqqimen.
Akk 37 d 1/37. Sbeɛṭac d uṭṭun i ɣef rehnen ugar, d tidet ɣef yimdanen.
Urar s tusnakt
Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.
Trehnem ɣef uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk →, tuzzya deffir tuzzya. Acḥal d taprubabilit ad d-yas rrbeḥ-nwen wis semmus deg tuzzya tis tam s tidet? U ad tesɛum semmus n rrbeḥ deg tam n tuzzyiwin timezwura?
Sken-d tifrat
Tiririt 12,9%, qrib 1 seg 8, i rrbeḥ wis semmus deg tuzzya tis tam. 33,4% i semmus n rrbeḥ ar dinna.
Rrbeḥ wis semmus deg tuzzya tis tam yebɣa ad yini snat n tɣawsiwin: tuzzya tis tam terbeḥ, u sa n tuzzyiwin timezwura sɛant s tidet ukkuẓ n rrbeḥ d kraḍ n lexsarat, s yal amyizwer. Llant 35 n tarrayin n usersu n ukkuẓ n rrbeḥ deg sa n tuzzyiwin.
Ihi taprubabilit d 35 × (18/37)⁵ × (19/37)³ = 35 × 0,02725 × 0,1354 = 12,9%.
I semmus n rrbeḥ ar tuzzya tis tam, rnut tiseddarin-nni n yiwet n tewsit i rrbeḥ wis semmus deg tuzzyiwin tis semmus, tis sḍis d tis sa: 2,7% + 7,0% + 10,8% + 12,9% = 33,4%. Imusnawen n tidaddanin qqaren-as abeṭṭu abinumyal n tuccḍiwin (negative binomial): acḥal n yiɛraḍen i yesra umḍan yettwasbedden n yigmaḍ yelhan. Taylor (2021) yexdem asteqsi-nni yiwen ɣef uḍebsi amarikani, 12,2%.
Taḍsa i usgunfu
Siḍnet tixxamin. Bḍut ɣef 37. Sgutet i yizrar. Yekfa.
Iɣbula
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.