NO.PZ2018122801000006
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：
D is correct.
考点Bayes' formula
解析
(Notices: if the wife did not receive the letter, she would not send response to the man.)
Note:
A: the wife received the letter; : the wife did not receive the letter;
B: the man received a response letter from his wife; : the man did not receive a response letter from his wife
The question "If the man does not receive a response letter from his wife, what is the probability that his wife received his letter?" is equal to figure out
考点：正态分布查表
解析： 题目说信可以成功寄到的概率是2/3，假设每次送信都是独立事件。同时假设妻子如果收到丈夫的信就一定会回复。问题问如果丈夫没有收到回信，那她的妻子收到丈夫的信的概率是多少？
首先丈夫没有收到回信的条件有两种情况：1.丈夫的寄信丢了，就是上面那个二叉树的下面一根，概率是1/3；2.丈夫的信寄到了，但是妻子的回信寄丢了（1/3），这种情况下概率为1/3*（2/3）=2/9
所以这两种情况下概率加和=1/3+2/9=5/9
根据贝叶斯公式，
如果丈夫没有收到回信，那她的妻子收到丈夫的信的概率=（2/9）/(5/9)=2/5
为什么不是这样？不太明白
