Bayes' Formula 貝氏公式

EF 為兩事件. 我們可將 E 表示成

EFEFc 很明顯的是互斥事件, 所以由 Axiom 3 可得

Equation (3.1) states that the probability of the event E is a weighted average of the conditional probability of E given that F has occurred and the conditional probability of E given that F has not occurred -- each conditional probability being given as much weight as the event that it is conditioned on has of occurring.

Example

Solution:
CK 分別表示學生答對題目和他確實知道答案的事件, 則