Koşullu olasılık

Koşullu olasılık kavramı, bir olayın gerçekleşme olasılığının hesaplanmasında ek bilginin kullanılmasına olanak tanır. Örneğin bir kişinin iki çocuğu olduğunu düşünürsek, her ikisinin de kız olma olasılığı 1/4 olur. Ancak birinin kız olduğunu önceden bilirsek, bu olasılık 1/3 olarak değişir. Ama herhangi biri değil de birincisi (yaşça büyük olan) kız olduğu biliniyorsa olasılık 1/2 olur. Yani bu iki durumda, her iki çocuğun da kız olma olasılığı, birinin kız olması koşullu olarak hesaplanır .

Tanım

Olasılık kuramında, A olayının, bir diğer B olayına koşullu olasılığı (veya B biliniyorken A'nın olasılığı), P(A | B) olarak tanımlanır;

Aynı kavramı ifade etmek için PB(A) hali de kullanılabilir. Bu tanımda veya P(A,B), A ile B olaylarının ortak olasılıklarını, yani her ikisinin de gerçekleşme olasılığını ifade eder.

Bağımsız olaylar

A ve B olayları birbirlerinden bağımsız olduklarında, birinin gerçekleştiğini bilmek doğal olarak diğerinın olasılık hesabına etki etmez. Bu durumda ortak olasılıkları basit bir çarpım halini alır:

dolayısıyla:

ve

Birbirini dışlayan olaylar

Bu durumda, her iki olayın birlikte gerçekleşme olasılığı sıfırlanır. Yani

Dolayısıyla:

ve

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