You are hereTavlada İstatistiğe Dayalı Olasılık Hesaplamaları
Tavlada İstatistiğe Dayalı Olasılık Hesaplamaları
Bu oyun hep cilveli, bana zarlar hileli! Tavladaki bütün olasılık hesaplamaları olasılığa dayanır.(Ne kadar ironik) Bu hesaplarda da (doğal olarak) 1 atma ihtimaliniz ile 4 atma ihtimaliniz birbirini eşittir. Ama gerçek zarlarda bu ihtimal çok ender olarak birbirine eşittir. Gerçek hayatta tüm zarlar hilelidir ve her zarın belli sayılara karşı yatkınlığı vardır.
Matematiksel nesneler fiziksel açıdan soyutlanmıştır. Doğruların kalınlığı düzlemlerin yüksekliği yoktur. Bir noktadan eşit uzaklıktaki noktaların geometrik olarak tanımlanan çemberler pürüzsüzdür. Zarlar mükemmel, kağıt desteleri iyi karıştırılmıştır.
Klasik tanımda yapılan soyutlama da bu anlamda matematiksel açıdan idealdir ve olasılık hesabına kolaylık sağlar. Ancak olasılık yaşama ilişkindir. Gerçek dünyada bütün zarlar hilelidir ve kusursuz zar yoktur. Her zarın az veya çok bir sayıya yatkınlığı vardır.
Kusursuz ve hilesiz bir zar attığınız varsayımıyla S, gerçekleşme şansları eşit (eş olasılıklı) sonuçlarından oluşan bir örnek uzayı ve A ise bu örnek uzayda tanımlı bir olayı göstersin.
A olayının gerçekleşme olasılığı olan P(A), bu yaklaşımda
Yani 3 atma olasılığınız,
Matematiksel nesneler fiziksel açıdan soyutlanmıştır. Doğruların kalınlığı düzlemlerin yüksekliği yoktur. Bir noktadan eşit uzaklıktaki noktaların geometrik olarak tanımlanan çemberler pürüzsüzdür. Zarlar mükemmel, kağıt desteleri iyi karıştırılmıştır. Klasik tanımda yapılan soyutlama da bu anlamda matematiksel açıdan idealdir ve olasılık hesabına kolaylık sağlar.
Ancak olasılık yaşama ilişkindir. Gerçek dünyada bütün zarlar hilelidir ve kusursuz zar yoktur. Her zarın az veya çok bir sayıya yatkınlığı vardır. Dolayısıyla gerçek hayatta bir zarı atma olasılığınız olan P(A), n(A)'nın n(S)'ye oranıyla zarın (A)'ya olan yatkınlık katsayısının k(A) çarpımına eşittir.
Yani klasik matematiğin aksine gerçek hayatta attığınız zarın 3 gelme ihtimali ile 5 gelme ihtimali eşit değildir.


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