Taprubabilit n yizrar deg rulit
Izrar iɣezfanen n yiwen yini ttwafen s waṭas. Ur sɛin ula d anamek i tuzzya d-iteddun.
Semmus n uzeggaɣ yeṭṭafaren: 2,7%. Mraw: 0,074%. Deg teɣimit n 200 n tuzzyiwin, azrar n sḍis n yiwen yini yettban-d tugget n wakud.
Acḥal n tikkal i d-yettas uzrar n lexsara
Rrehn s lexlaṣ imsawi ɣef uḍebsi s yiwen yilem yettexsar 19 n tuzzyiwin seg 37. Yal ajerriḍ d taprubabilit ara xesrent akk tuzzyiwin n yiwen uzrar, d wayen yexser ar tura umurar n Martingale, i yessnernayen rrehn s snat deffir yal lexsara.
| lexsarat ṭṭafarent | taprubabilit | qrib 1 seg | lexsara ar tura | rrehn d-iteddun |
|---|---|---|---|---|
| 1 | 51,4% | 2 | $1 | $2 |
| 2 | 26,4% | 4 | $3 | $4 |
| 3 | 13,5% | 7 | $7 | $8 |
| 4 | 7,0% | 14 | $15 | $16 |
| 5 | 3,6% | 28 | $31 | $32 |
| 6 | 1,8% | 55 | $63 | $64 |
| 7 | 0,94% | 106 | $127 | $128 |
| 8 | 0,48% | 207 | $255 | $256 |
| 9 | 0,25% | 403 | $511 | $512 |
| 10 | 0,13% | 784 | $1 023 | $1 024 |
| 11 | 0,065% | 1527 | $2 047 | $2 048 |
| 12 | 0,034% | 2974 | $4 095 | $4 096 |
| 13 | 0,017% | 5792 | $8 191 | $8 192 |
| 14 | 0,0089% | 11279 | $16 383 | $16 384 |
| 15 | 0,0046% | 21965 | $32 767 | $32 768 |
Taprubabilit d 19/37 yettwasgeten s yiman-is yiwet n tikkelt i yal lexsara, seg yiwet n tuzzya yettwafernen. Taɣimit taɣezfant tesɛa aṭas n tuzzyiwin anda yezmer ad yebdu wazrar am wa, ihi deg yiwet n tmeddit taprubabilit-is tugar aṭas ayen i d-yesskan yiwen ujerriḍ.
Yiwen wazrar
TaprubabilittusnaktTaprubabilitAzal n yiwen ugmuḍ ad d-yeḍru, seg 0 ɣer 1 neɣ seg 0% ɣer 100%. Yiwen wuṭṭun: 1/37 = 2,70%.Ɣer akk → belli k n tuzzyiwin d-iteddun akk d azeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → d (18/37)ᵏ. Sin: 23,7%. Semmus: 2,7%. Mraw: 0,074%, qrib 1 seg 1 350. Ɛecrin: 1 seg 1,8 n yimelyunen. Sḍis u ɛecrin, arikur n Monte Carlo: 1 seg 137 n yimelyunen. Tigi d tiprubabiliyin n wazrar yettwasbeddren i yebdan deg tuzzya yettwasbeddren, d asteqsi ur yettesteqsay qrib yiwen.
Deg teɣimit
Asteqsi i bɣan imdanen d «ad d-yettban wazrar n k deg kra n umkan deg teɣimit-iw?», tiririt tugar aṭas (18/37)ᵏ acku taɣimit n 200 n tuzzyiwin tettak qrib 200 n yimukan ideg yezmer ad yebdu wazrar. Azrar n sḍis neɣ ugar n yiwen yini, azeggaɣ neɣ aberkanrrehnAberkanRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen iberkanen. S tefransist: noir.Ɣer akk →, yettban-d deg teɣimit n 200 n tuzzyiwin qrib 94% n wakud; tam neɣ ugar qrib 47%; mraw neɣ ugar qrib 14%. Init-d yini uqbel, tiprubabiliyin ad ṣubbent, ɣer qrib 75%, 27% d 7%. Amurar ara yeqqimen tameddit akk ad iwali izrar iɣezfanen yal tameddit.
Ayɣer yeɛna Martingale
Yal anagraw n usnernitastratijitAnagraw n usnerniYal alugen i yettbeddilen rrehn ɣef leḥsab n yigmaḍ yezrin. Asnerni deffir lexsara yessali-t deffir lexsara, asnerni deffir rrbeḥ deffir rrbeḥ.Ɣer akk → deffir lexsara yesɛa teɣzi n wazrar i t-yerrẓen: sḍis n lexsarat seg $10 n tazwara s talast n $500, mraw i FibonaccitastratijitFibonacciAnagraw n usnerni i yeḍfaren umuɣ 1, 1, 2, 3, 5, 8, 13…: yiwen usurif ɣer zdat deffir lexsara, sin ɣer deffir deffir rrbeḥ.Ɣer akk →, semmus i usnerni s kraḍ ɣef ddzinatrrehnDdzina1–12, 13–24 neɣ 25–36, ixelleṣ 2:1.Ɣer akk →. Taprubabilit n wazrar n sḍis n lexsarat ɣef lexlaṣ imsawi d (19/37)⁶ ≈ 1,8% i yal aneɛruḍ, yerna taɣimit n 200 n tuzzyiwin tesɛa ahat 100 n yineɛruḍen, ihi aṛeẓ yettas-d qrib deg ukkuẓ n tɣimiyin seg semmus s teɣzi-a. Taprubabilit n yizrar deg rulit d ssebba ɣef wacu aɣelluy-a mačči d ayen yettwafen qlil.
Uṭṭunen yeḥman d yisemmaḍen
Yiwen leḥsab yettwasnas ɣef yiwen wuṭṭunrrehnYiwen wuṭṭunYiwen wuṭṭun kan, ixelleṣ 35:1.Ɣer akk →. Deg 300 n tuzzyiwin amḍan yettwaṛǧan i yal uṭṭun d 8,1; abeɛɛed alugantusnaktAbeɛɛed aluganAẓar amkuẓ n tavaryans; ameccaq n umata gar ugmuḍ d wazal yettwaṛǧan.Ɣer akk → d qrib 2,8. Kra n wuṭṭun ad d-yesskan 15 n tuṭṭfiwin, wayeḍ 2, s zzher kan, yal tikkelt. Tafelwit n yigmaḍ i yesbeggnen uṭṭunen «yeḥman» tesbeggin aqerru n ubeṭṭu amagnu. Tanarit tessefhem acḥal n tuzzyiwin i ilaqen uqbel uṭṭun yeḥmanlexrafaUṭṭun yeḥmanUṭṭun i d-yeffɣen ugar n wayen yettwaṛǧan melmi kan. Ɣef uḍebsi imsawi ur d-yettbeggin acemma.Ɣer akk → ad yesɛu anamek (igiman, seg yiwen uḍebsi yettwassnen).
Tamanit d ayen akk
Azrar n mraw n uzeggaɣ ur yettarra ara aberkan s taprubabilit meqqren, ur yettarra ara daɣen azeggaɣ. Sin yid-sen d 18/37. Izrar d taɣara n yigmaḍ igacuranen yemḍafaren, yerna ad ǧǧen ccek ma ulac-iten: 200 n tuzzyiwin war azrar yugaren ukkuẓ ad ilint d abeggen n uɣecceḍ ugar n tid yesɛan azrar n tnac.
Tasemselt
Isteqsiyen
26 n uberkan deg Monte Carlo ass n 18 ɣuct 1913 d win yettwassnen. 32 n uzeggaɣ yeṭṭafaren, nnan-d belli yeḍra deg lkazinu tamarikanit deg 1943. Sin yid-sen mṣadan d zzher ma nwala acḥal n tuzzyiwin i xeddment lkazinu.
D 18/37 ɣef sin. Rhent ayen i d-yenna uɣawas-nwen, neɣ ur ttrehinet ara.
Ala. Amyal yettban-d mi ara d-ffɣent kra n texxaminibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk → s waṭas deg yigiman n tuzzyiwin, mačči deg yizrar n yini.
Urar s tusnakt
Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.
Acḥal n tuzzyiwin n uḍebsi awrupi i yesran, s ulemmas, qbel ad d-ffɣen akk 37 n wuṭṭunen ma drus yiwet n tikkelt?
Sken-d tifrat
Tiririt Qrib 155 n tuzzyiwin s ulemmas; azal n tlemmast d 147.
Ḥesbet arraǧu uṭṭun amaynut s wuṭṭun amaynut. Tuzzya tamezwarut tesskan-d yal tikkelt uṭṭun amaynut. Mi ara twalim 1 n wuṭṭun, 36 n texxaminibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk → deg 37 d timaynutin, ihi uṭṭun amaynut d-iteddun yesra 37/36 n tuzzyiwin s ulemmas. Mi ara twalim k n wuṭṭunen, yesra 37/(37 − k).
Rnut arraǧu: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4,20 = 155,5 n tuzzyiwin.
Tuget-is d taggara. Uṭṭun aneggaru iman-is yesra 37 n tuzzyiwin s ulemmas, semmus ineggura qrib 85. Ɣef uḍebsi amarikani, amatu-nni yettak-d qrib 161. Wa d ugur n umejmaɛ n yikupunen; alemmas-nni yiwen d-yettas seg leḥsab amagnu.
Deg 37 n tuzzyiwin n uḍebsi awrupi, yiwet i yal taxxamt, acḥal n wuṭṭunen yemgaraden ara tettṛaǧum ad twalim?
Sken-d tifrat
Tiririt Qrib 23,6. Qrib tulut n wuṭṭunen, qrib 13, ur d-ttbanen ara akk.
Ṭṭfet yiwen wuṭṭun, amedya 17. Deg yal tuzzya ur d-yettban ara s tprubabilit n 36/37, ihi ur d-yettban ara deg 37-nni n tuzzyiwin s tprubabilit n (36/37)³⁷ ≈ 0,363.
Yal uṭṭun yesɛa taprubabilit-nni yiwet, ihi s ulemmas 37 × 0,363 ≈ 13,4 n wuṭṭunen ulac-iten u 37 − 13,4 ≈ 23,6 d-ttbanen, aṭas seg-sen snat n tikkal neɣ ugar.
Imuraren n rulit qqaren-as alugen n tulut. Mačči d alugen, d leḥsab kan n yiɛawaden: deg uzrar ɣezzifen am uḍebsi, qrib tulut n wuṭṭunen ur d-ttbanen ara, ɣef uḍebsi imsawi am wiyaḍ. Ɣef 38 n texxamin, tasgunt d (37/38)³⁸ ≈ 0,363 daɣen; i uḍebsi ameqqran terseḥ ɣer 1/e ≈ 0,368.
Amdakkel yesskan-awen-d snat n tebdarin n 50 n yiniten, azeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → neɣ aberkanrrehnAberkanRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen iberkanen. S tefransist: noir.Ɣer akk →, qqaren d-ttasent seg uḍebsi war ilmawenaḍebsiIlemTaxxamt 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 →. Yiwet tbeddel yini 25 n tikkal u azrar-is aɣezfan akk d sḍis. Tayeḍ tbeddel 35 n tikkal u werǧin tɛedda kraḍ. Anta i yettwasnulfan?
Sken-d tifrat
Tiririt Tis snat. Tabdart n tidet tbeddel qrib 24 neɣ 25 n tikkal. Tabdart s 35 n yibeddilen d-tettban qrib yiwet n tikkelt deg 500 n tebdarin, u tin war azrar yugaren kraḍ qrib snat n tikkal deg 100.
Yal yini amaynut yettɛawad win yezrin neɣ ibeddel, azgen d wezgen, ihi 49 n tegnatin n ubeddel ttak-d 24,5 n yibeddilen s ulemmas, ugar neɣ drus qrib 3,5. Xemsa u tlatin d kraḍ n tseddarin-a nnig walemmas; aḍebsi imsawi yettak-d aṭas-a n yibeddilen qrib yiwet n tikkelt deg 500 n tebdarin.
Izrar qqaren-d ayen-nni yiwen. Tabdart n tidet n 50 tesɛa azrar n ukkuẓ neɣ ugar qrib 98% n wakud, u azrar-is aɣezfan akk s waṭas d semmus neɣ sḍis.
Medden i wumi yettwasuter ad snulfun tabdart tagacurant beddlen aṭas, acku azrar n ukkuẓ neɣ n semmus yettban-asen d talɣa. Taylor (2021) yesskan-d ayen-nni yiwen deg tebdarin n tegrin n uṣurdi i snulfan yinelmaden: zzher n tidet yesɛa izrar ugar n wayen i ɣillen medden.
Adlis n tmucuha n lkazinu yettmeslay ɣef umurar i wumi d-yeffeɣ wuṭṭun-is semmus n tikkal ṭṭafarent u yenna-d ur yeḍri ara wayen yugaren aya. Acḥal ur yettili ara waya ɣef uḍebsi awrupi? D acḥal n tikkal ilaq ad yeḍru deg yiwet n lkazinu s 20 n ṭṭabliyat, yal yiwet tettezzi 40 n tikkal deg ssaɛa, ass d yiḍ?
Sken-d tifrat
Tiririt Uṭṭun yettwasemman semmus n tikkal ṭṭafarent: 1 seg 69 n yimelyunen. Yal uṭṭun i d-yuɣalen ukkuẓ n tikkal nniḍen deffir tikkelt tamezwarut: 1 seg 1,87 n yimelyunen. Lkazinu-nni tezzi qrib 7 n yimelyunen n tikkal deg useggas, ihi ilaq ad twali azrar n semmus kraḍ neɣ ukkuẓ n tikkal deg useggas.
Uṭṭun yettwasemman yeffeɣ-d s tprubabilit n 1/37 deg yal tuzzya, ihi semmus ṭṭafaren sɛan taprubabilit n (1/37)⁵ = 1 seg 69 343 957. Maca ulac win isemman uṭṭun zik. Akken yebɣu yili win d-yeffɣen d amezwaru, ukkuẓ n tuzzyiwin d-iteddun ilaq ad t-ɛawdent: (1/37)⁴ = 1 seg 1 874 161.
20 n ṭṭabliyat × 40 n tuzzyiwin × 24 n yisragen × 365 n wussan = 7 008 000 n tuzzyiwin deg useggas. Yal tuzzya tezmer ad tebdu azrar, ihi lkazinu tettṛaǧu 7 008 000/1 874 161 ≈ 3,7 n yizrar n semmus deg useggas.
Ulac tira tunṣibt n wayen yugaren deg wanaw-a, u ur tettusra ara: ayen ur nettili ara ɣef yiwet n ṭṭabla d ayen n yal ass ɣef lkazinu meṛṛa, u timucuha ttwanant-d ɣef ṭṭabla anda yeḍra. Tamacahut, deg Goldman (2007), tella ɣef uḍebsi s sin yilmawen, anda imḍanen d 1 seg 79 n yimelyunen d 1 seg 2,09 n yimelyunen.
Taḍsa i usgunfu
Izrar iɣezfanen d wamek i yettban ugacuran.
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.