Multiplication Rule for Probability.
两个事件同时发生的概率，用乘法（why？）
Suppose we ask the question “What is the probability of both A and B happening?” The answer to this question is a joint probability, denoted P(AB) (read: “the probability of A and B”).
If we think of the probability of A and the probability of B as sets built of the outcomes of one or more random variables, the joint probability of A and B is the sum of the probabilities of the outcomes they have in common.
For example, consider two events: the stock earns a return above the risk-free rate (A) and the stock earns a positive return (B). The outcomes of A are contained within (a subset of) the outcomes of B, so P(AB) equals P(A). We can now state a formal definition of conditional probability that provides a formula for calculating it.
Definition of Conditional Probability. The conditional probability of A given that B has occurred is equal to the joint probability of A and B divided by the probability of B (assumed not to equal 0).
条件概率公式
为什么事件 B 发生的条件下发生事件 A 的概率等于两个事件同时发生的概率除以事件 B 发生的概率？
因为：
- 概率的本质是频率
- 频率的基本写法就是
- 除法的本质是分子在分母里占多大的面积
- 以事件 B为母集，在此母集中，AB 同时发生的频次有多少，则两者之商为P(A|B)
看概率一定厘清母集（全集）与子集（subset）的概念与角色。