Ugur: aḍebsi n wass n tlalit
Acḥal n tuzzyiwin uqbel ad d-yuɣal kra n wuṭṭun? Drus aṭas n wayen i ɣillen tugget n yimdanen.
Ugur n wass n tlalit ɣef uḍebsi n 37 n texxaminibenkanTaxxamtYiwet seg 37 n texxamin s wuṭṭunen ɣef uqerru yettezzin. Daɣen: slot, cup.Ɣer akk →: deffir 8 n tuzzyiwin kan, taprubabilit tugar azgen belli kra n wuṭṭun yeffeɣ-d yakan snat n tikkal. Imuraren ɣerren tuɣalin am talɣiwin; d tikli yettwaṛǧan n uḍebsi imsawi.
Ugur
Zzit aḍebsi awrupi imsawi. Acḥal n tuzzyiwin alamma 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 ma drus snat n tuzzyiwin sskanent yiwen wuṭṭun tezgar azgen? Tugget n yimuraren ttɣilen qrib 18 neɣ 19, azgen n 37. Tiririt d 8.
Tifrat
Ḥesbet taprubabilit ulac tuɣalin, kkset-itt seg yiwen. Deffir k n tuzzyiwin, p(akk mgaraden) = (37/37)(36/37)(35/37)…((38 − k)/37). I k = 8: 1 × 0,973 × 0,946 × 0,919 × 0,892 × 0,865 × 0,838 × 0,811 ≈ 0,44, ihi p(kra n tuɣalin) ≈ 0,56. I k = 14 d 0,93; i k = 20 d 0,996. Aḥulfu yettecceḍ acku amḍan n tyugiwin n tuzzyiwin yettnerni am k², yerna yal tayuga tezmer ad temṣada.
Ayɣer yesɛa azal ɣef ṭṭabla
Tafelwit n yigmaḍ n 20 n wuṭṭunen ineggura ad d-tesskan qrib yal tikkelt ma drus yiwet n tuɣalin, s waṭas snat neɣ kraḍ. Imuraren walan «17 yeffeɣ-d snat n tikkal deg mraw n tuzzyiwin», nnan 17 yeḥma; leḥsab n wass n tlalit yeqqar belli tuɣalin deg mraw n tuzzyiwin teḍṛu 74% n wakud, yerna uṭṭun i d-yuɣalen d agacuran. Talɣa d tidet; anamek ala.
Ugur d-iteddun
Acḥal n tuzzyiwin alamma uṭṭun yettwasbedden, am 17, yeffeɣ-d snat n tikkal? D asteqsi nniḍen s tririt meqqren aṭas: araǧu yettwaṛǧan d 74 n tuzzyiwin, yerna taprubabilit n sin n 17 deg 20 n tuzzyiwin d qrib 10%. Amgired gar «kra n wuṭṭun yuɣal-d» (8 n tuzzyiwin) d «uṭṭun-a yuɣal-d» (74 n tuzzyiwin) d amgired akk gar telɣa i twalam deffir d wayen i d-tettinim uqbel.
Ɛerḍet-t
Sselkmet Urar n uɛraḍ i mraw n tuzzyiwin, walit amazray. S umata ad tili tuɣalin. Sselkmet-it tikkelt nniḍen. Uṭṭun i d-yuɣalen ad yili d wayeḍ. Xedmet aya mraw n tikkal, ihi twalam ugur n wass n tlalittusnaktUgur n wass n tlalitAcḥal n yimdanen i ilaqen send ad yili, s tprubabilit, sin i yesɛan yiwen wass n tlalit, neɣ acḥal n tuzzyiwin send ad d-yuɣal yiwen wuṭṭun. Ɣef uḍebsi n 37 n texxamin, 8 n tuzzyiwin qadrent akken taprubabilit ad tili ugar n uzgen.Ɣer akk →; xedmet-t agim n tikkal (isimulaturen zemren) ihi tektalem-t.
Tasemselt
Isteqsiyen
S timmad-is, s 37 n texxamin deg umkan n 365 n wussan. 23 n yimdanen ttaken 50% i wussan n tlalit; 8 n tuzzyiwin ttaken 56% i uḍebsi.
50% deffir qrib 19 n tuzzyiwin. Mazal d ayen n yal ass.
Ala. Igiman n tuzzyiwin seg yiwen uḍebsi zemren; tuɣalin werǧin.
Urar s tusnakt
Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.
Tafelwit n yigmaḍ ɣer tama n uḍebsi amarikani tesskan-d 16 n tuzzyiwin tineggura. Acḥal i tezmer ad tili ulac uṭṭun i d-yettbanen snat n tikkal fell-as?
Sken-d tifrat
Tiririt Qrib 2,5%: qrib 39 n tfelwiyin seg 40 sskanent-d ma drus yiwen wuṭṭun yettwalsen.
Ddut tuzzya s tuzzya. Tuzzya tamezwarut tezmer ad tili d acu kan. Tis snat ilaq ad tt-tɛeddi: 37 n tegnatin deg 38. Tis kraḍ ilaq ad tɛeddi i snat: 36 deg 38. Tis sṭac ilaq ad tɛeddi xmesṭac n wuṭṭunen: 23 deg 38.
Sgetet: 38/38 × 37/38 × 36/38 × … × 23/38 ≈ 0,0246.
Tafelwit war uṭṭun yettwalsen d tin ur nettili ara aṭas. Tafelwit s wuṭṭun yettwalsen ur d-tettini acemma ɣef uḍebsi.
Deg mraw n tuzzyiwin n uḍebsi awrupi, acḥal d taprubabilit ad d-yeffeɣ 17 semmus n tikkal kan? Ad d-yeffeɣ yiwen wuṭṭun, akken yebɣu yili, semmus n tikkal neɣ ugar? U ad d-yeffeɣ yiwen wuṭṭun ma drus kraḍ n tikkal deg ukkuẓ n tuzzyiwin?
Sken-d tifrat
Tiririt 17 semmus n tikkal kan: 1 seg 315 576. Yiwen wuṭṭun semmus n tikkal neɣ ugar: qrib 1 seg 8 333. Yiwen wuṭṭun kraḍ n tikkal neɣ ugar deg ukkuẓ n tuzzyiwin: 1 seg 349.
17 semmus n tikkal: fernet anta semmus seg mraw-nni n tuzzyiwin, 252 n tarrayin, yal yiwet s tprubabilit n (1/37)⁵ × (36/37)⁵. Akk, 1 seg 315 576.
Yiwen wuṭṭun: yal yiwen seg 37 n wuṭṭunen yesɛa taprubabilit n 1 seg 308 325 n semmus n tikkal neɣ ugar, ayen i d-yettaken 37 deg 308 325, neɣ 1 seg 8 333. Tagnit ur nettili ara n sin wuṭṭunen s semmus n tikkal yal yiwen tettwaḥseb snat n tikkal, maca tukksa-s ur tbeddel acemma s tseddi-a n leḥsab.
Kraḍ n tikkal deg ukkuẓ n tuzzyiwin: i yiwen wuṭṭun, 4 × 36 + 1 = 145 seg 37⁴ n yigmaḍ i yezmren ad ilin; i yal yiwen seg 37 n wuṭṭunen, 145/37³ = 1 seg 349.
I uḍebsi s sin yilmawenaḍebsiIlemTaxxamt 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 →, imḍanen-nni d 1 seg 359 275, 1 seg 9 243 d 1 seg 368. Amgired gar «17» d «yiwen wuṭṭun» d ugur n wass n tlalittusnaktUgur n wass n tlalitAcḥal n yimdanen i ilaqen send ad yili, s tprubabilit, sin i yesɛan yiwen wass n tlalit, neɣ acḥal n tuzzyiwin send ad d-yuɣal yiwen wuṭṭun. Ɣef uḍebsi n 37 n texxamin, 8 n tuzzyiwin qadrent akken taprubabilit ad tili ugar n uzgen.Ɣer akk → tikkelt nniḍen: llant 37 n tarrayin n twaɛjebt.
Taḍsa i usgunfu
Kra yettuɣal-d zik. Kra-nni d agacuran.
Iɣbula
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Wizard of Odds. “Ask the Wizard”, isteqsiyen ɣef rulit.