Masalo: Giraangirta Dhalashada
Imisa wareeg ka hor inta lambar uun uusan soo noqon? Aad uga yar inta dadka intooda badani qiyaasaan.
Masalada dhalashada ee giraangir 37 godqalabGodMid ka mid ah 37-ka qol ee lambarrada leh ee rotor-ka. Sidoo kale: slot, cup.Akhri dhammaan → leh: kadib kaliya 8 wareeg waxaa jira fursad ka badan kala bar in lambar uun horay laba jeer u soo baxay. Ciyaartoydu soo noqoshada waxay u akhriyaan qaabab; waa dhaqanka la filayo ee giraangir caddaalad ah.
Masalada
Wareeji giraangir Yurub ah oo caddaalad ah. Imisa wareeg ilaa itimaalkaxisaabItimaalFursadda natiijo, 0 ilaa 1 ama 0% ilaa 100%. Hal lambar: 1/37 = 2.70%.Akhri dhammaan → in ugu yaraan laba wareeg ay muujiyeen isla lambar uu ka badnaado kala bar? Ciyaartoyda intooda badani waxay qiyaasaan meel ku dhow 18 ama 19, kala bar 37. Jawaabtu waa 8.
Xalka
Xisaabi itimaalka soo noqosho la'aanta oo ka jar hal. Kadib k wareeg, p(dhammaan kala duwan) = (37/37)(36/37)(35/37)…((38 − k)/37). Marka k = 8: 1 × 0.973 × 0.946 × 0.919 × 0.892 × 0.865 × 0.838 × 0.811 ≈ 0.44, sidaas darteed p(soo noqosho uun) ≈ 0.56. Marka k = 14 waa 0.93; marka k = 20 waa 0.996. Dareenku wuu khaldamaa sababtoo ah tirada lammaanaha wareegyada waxay u koraan sida k², lammaane kastana wuu isku eekaan karaa.
Sababta ay miiska muhiim ugu tahay
Looxa natiijooyinka ee 20-ka lambar ee ugu dambeeyay wuxuu had iyo jeer muujiyaa ugu yaraan hal soo noqosho, inta badan laba ama saddex. Ciyaartoydu waxay arkaan “17 laba jeer ayuu soo baxay toban wareeg gudahood” waxayna go'aamiyaan in 17 kulul yahay; xisaabta dhalashadu waxay leedahay soo noqosho toban wareeg gudahood ah waxay dhacdaa 74% waqtiga, lambarka soo noqdayna waa nasiib. Qaabku waa dhab; macnuhu ma aha.
Masalada xigta
Imisa wareeg ilaa lambar gaar ah, tusaale 17, uu laba jeer soo baxo? Taasi waa su'aal ka duwan oo jawaab aad u weyn leh: sugitaanka la filayo waa 74 wareeg, itimaalka laba 17 ah 20 wareeg gudahoodna waa qiyaastii 10%. Farqiga u dhexeeya “lambar uun baa soo noqda” (8 wareeg) iyo “lambarkan baa soo noqda” (74 wareeg) waa farqiga oo dhan ee u dhexeeya qaab aad dabadeed dareento iyo saadaal aad horay u sameyso.
Isku day
Ciyaarta Demo u socodsii toban wareeg oo eeg taariikhda. Inta badan waxaa jiri doona soo noqosho. Mar kale socodsii. Lambarka soo noqday wuu kala duwanaan doonaa. Sidan toban jeer samee, waxaad aragtay masalada dhalashadaxisaabMasalada dhalashadaInta qof ee loo baahan yahay ka hor inta aysan laba qof u badan tahay inay wadaagaan maalin dhalasho, ama inta wareeg ka hor inta aysan lambar u badan tahay inuu soo noqdo. Giraangir 37 god leh, 8 wareeg ayaa ku filan fursad ka badan kala bar.Akhri dhammaan →; kun jeer samee (jilayaashu way awoodaan), waxaad cabbirtay.
Qaacido
Su'aalo
Si sax ah, iyadoo 37 god ay jiraan halkii 365 maalmood. 23 qof waxay bixiyaan 50% dhalashooyinka; 8 wareeg waxay bixiyaan 56% giraangirta.
50% kadib qiyaastii 19 wareeg. Weli waa caadi.
Maya. Kumanaan wareeg oo hal giraangir ah ayaa tilmaami kara; soo noqoshadu weligeed ma tilmaanto.
Madadaalo Xisaabeed
Marka hore adigu isku day. Xal kasta waa qarsoon yahay; fur marka aad diyaar u tahay.
Looxa natiijooyinka ee ku ag yaal giraangir Mareykan ah wuxuu muujiyaa 16-kii wareeg ee ugu dambeeyay. Intee in le'eg ayay u badan tahay in aan lambar ku soo noqon laba jeer?
Muuji xalka
Jawaab Qiyaastii 2.5%: qiyaastii 39 looxood 40 kiiba waxay muujiyaan ugu yaraan hal soo noqosho.
Wareeg wareeg u soco. Wareegga koowaad wuxuu noqon karaa wax kasta. Ka labaad waa inuu seegaa: 37 fursadood 38 kiiba. Ka saddexaad waa inuu labadaba seegaa: 36 38 kiiba. Ka lix iyo tobnaad waa inuu seegaa shan iyo toban lambar: 23 38 kiiba.
Isku dhufo: 38/38 × 37/38 × 36/38 × … × 23/38 ≈ 0.0246.
Looxa aan soo noqosho lahayn ayaa ah kan dhifka ah. Loox soo noqosho leh waxba kama sheego giraangirta.
Toban wareeg oo giraangir Yurub ah, waa maxay itimaalka in 17 ay soo baxdo si sax ah shan jeer? In lambar, lambar kasta, uu soo baxo shan jeer ama ka badan? Iyo in lambar uu soo baxo ugu yaraan saddex jeer afar wareeg gudahood?
Muuji xalka
Jawaab 17 si sax ah shan jeer: 1 315,576 kiiba. Lambar uun shan jeer ama ka badan: qiyaastii 1 8,333 kiiba. Lambar uun saddex jeer ama ka badan afar wareeg gudahood: 1 349 kiiba.
17 shan jeer: dooro shanta ka mid ah tobanka wareeg, 252 hab, mid kasta itimaal (1/37)⁵ × (36/37)⁵. Wadar ahaan, 1 315,576 kiiba.
Lambar uun: mid kasta oo ka mid ah 37-ka lambar wuxuu leeyahay itimaal 1 308,325 kiiba oo shan ku dhac ama ka badan ah, taas oo bixisa 37 308,325 kiiba, ama 1 8,333 kiiba. Xaaladda dhifka ah ee laba lambar oo mid kastaa shan ku dhac leeyahay ayaa laba jeer la tiriyaa, laakiin ka saariddeedu waxba ma beddesho saxnaantan.
Saddex jeer afar wareeg gudahood: hal lambar, 4 × 36 + 1 = 145 ka mid ah 37⁴ natiijo ee suurtagalka ah; mid kasta oo ka mid ah 37-ka lambar, 145/37³ = 1 349 kiiba.
Giraangir laba-ebergiraangirEberHal godka cagaaran ee aan daboolin sharad lacag isle'eg ah, dersin ama tiir; isha faa'iidada kasiinada. Sidoo kale: single zero, 0.Akhri dhammaan → ah, tirooyinka u dhigma waa 1 359,275 kiiba, 1 9,243 kiiba iyo 1 368 kiiba. Farqiga u dhexeeya “17” iyo “lambar uun” waa mar kale masalada dhalashadaxisaabMasalada dhalashadaInta qof ee loo baahan yahay ka hor inta aysan laba qof u badan tahay inay wadaagaan maalin dhalasho, ama inta wareeg ka hor inta aysan lambar u badan tahay inuu soo noqdo. Giraangir 37 god leh, 8 wareeg ayaa ku filan fursad ka badan kala bar.Akhri dhammaan →: waxaa jira 37 hab oo lagula yaabo.
Kaftan yar
Wax baa goor hore soo noqda. Waxaasi waa nasiib.
Ilaha
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Wizard of Odds. “Ask the Wizard”, su'aalaha roulette.