Question

你好，有一道统计学的题目，想要提问，谢谢～

4. An exit poll during a recent election revealed that 52% of those voting were women and 48% were men. The results also showed that 70% of the women voting favored Democratic candidates while only 40% of the men favored Democratic candidates. There were only two parties (Democratic Party and Republican Party) from which voters were able to choose. Each and every voter chooses one candidate from either party.

(a) If you select one person randomly in the exit poll sample, what is the probability that this person is a woman who voted for a Democratic candidate?

这道题，标准答案给的是：选民为女性并且投给民主党候选人的交集的概率[即P(M☊D)]是0.364

我理解的是，这道题目让求的是：在投给民主党候选人的条件下选民为女性的条件概率[即P(W|D)]

所以有点想不明白，就这道题而言我思路错误的原因是什么。以及，究竟什么时候求条件概率，什么时候求交集呢？ 麻烦您了，谢谢🙏

Answer 1

P(B/A)条件概率是：在事件A发生的前提下，B发生的概率
P(AB)是A, B事件均发生的概率，
两者的样本空间发生了变化，前者是增加了一个前提：A发生了。
后者A,B之间没有任何的关系。
注意看此题：
If you select one person randomly in the exit poll sample, what is the probability that this person is a woman who voted for a Democratic candidate?
它给你的预设条件就是：在投给民主党的前提下。
只要遇见给你假设前提的，你都认识是需要求条件概率。