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🧸苏小糖yb💚 · 2024年05月01日

这个题目答案是2/5还是1/3

NO.PZ2023091601000009

问题如下:

In country X, the probability that a letter sent through the postal system reaches its destination is 2/3. Assume that each postal delivery is independent of every other postal delivery, and assume that if a wife receives a letter from her husband, she will certainly mail a response to her husband. Suppose a man in country X mails a letter to his wife (also in country X) through the postal system. If the man does not receive a response letter from his wife, what is the probability that his wife received his letter?

选项:

A.

1/3

B.

3/5

C.

2/3

D.

2/5

解释:


这个题目答案是2/5还是1/3

,如果是2/5那么算式分母是.什么函义

1 个答案

李坏_品职助教 · 2024年05月01日

嗨,从没放弃的小努力你好:


答案是2/5.

这道题是问你,在丈夫没有收到回信的条件下,求出妻子收到丈夫来信的概率。这属于典型的贝叶斯条件概率问题,所以要用到贝叶斯条件概率公式。


设:

A表示妻子收到丈夫来信,B表示丈夫没有收到回信。本题也就是让我们求出P(A|B),而P(A|B) = P(AB) / P(B)。算式的分母就是B事件单独发生的概率P(B)。

B单独发生有两种可能:1. 丈夫一开始写的信寄丢了,概率是1/3。 2.丈夫一开始的信成功寄到妻子手里,但妻子的回信寄丢了,概率是2/3 * 1/3.

把两个情况加起来 = 1/3 + 2/3 * 1/3 = 5/9.也就是分母求的P(B)


而分子求的是P(AB) = 1/3 * 2/3 = 2/9.



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