如果A可以被partition成多個FINITE disjoint events
舉例來說
Suppose we put five different dice into a hat. The dice have the following number of sides: 4, 6, 8, 12, 20. When we choose a die from the hat, each of the five of the dice are equally likely to appear. Suppose that a “3” appears. What is the probability it was the 4-sided die that was chosen?
設B為3出現的event
A為4面骰子被選中個事件
我們要求的是P(A|B)，不過事實上選骰子的sample space可以partition成5個disjoint events，4面骰子選中只是其中之一，所以如果要用此邏輯的話，可以套用此bayes theorem變形：
所以假設四面骰子被選中的事件為A1:
其實這個看法跟筆記五中寫的一樣，只是筆記五中的對A的partion只有兩個A和其complement，這邊可以partition成五個。得出的式子也會一樣。
如果A可以被partition成多個INFINITE disjoint events
沒有留言:
張貼留言