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Infinite · 2020年02月07日

问一道题：NO.PZ2018122801000006

  1. FRM I
  2. Quantitative

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; A ¯ : the wife did not receive the letter;

B: the man received a response letter from his wife; B ¯ : 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 P(A| B ¯ )  

P(A| B ¯ )= P(A B ¯ ) P( B ¯ ) = P( B ¯ )×P( B ¯ |A) P( B ¯ )×P( B ¯ |A)+P( B ¯ )×P( B ¯ | A ¯ )  

= (2/3)×(1/3) (2/3)×(1/3)+(1/3)×1 = 2 5  

问的是妻子收到信的概率，为什么是收到的概率乘以NO RESPONSE 2/3*1/3 而不是2/3*2/3呢？请老师帮忙解答一下，谢谢

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1 个答案

品职答疑小助手雍 · 2020年02月07日

同学你好，首先要满足的是丈夫没收到回信这个事情，没收到回信有两种情况：1.丈夫的信寄丢了（1/3），2.丈夫的信寄到了的情况下，妻子回信寄丢了（2/3*1/3）=2/9。

也就是这个前提占所有可能性的5/9,那么在这个情况下，妻子收到信的概率（也就是第二种情况）就是（2/9）/ （5/9）=2/5。

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NO.PZ2018122801000006问题如下 In country X, the probability tha letter sent through the postsystem reaches its stination is 2/3. Assume theapostlivery is inpennt of every other postlivery, anassume thif a wife receives a letter from her husban she will certainly mail a response to her husban Suppose a man in country X mails a letter to his wife (also in country X) through the postal system. If the mes not receive a response letter from his wife, whis the probability thhis wife receivehis letter? 1/3 3/5 2/3 2/5 is correct. 考点 Bayes' formul解析 (Notices: if the wife not receive the letter, she woulnot senresponse to the man.) Note: the wife receivethe letter; ¯ : the wife not receive the letter; the mreceivea response letter from his wife; ¯ : the mnot receive a response letter from his wife The question \"If the mes not receive a response letter from his wife, whis the probability thhis wife receivehis letter?\" is equto figure out P( ¯ ) 考点正态分布查表 P( ¯ )= P( ¯ ) P( ¯ ) = P( ¯ )×P( ¯ | P( ¯ )×P( ¯ |A)+P( ¯ )×P( ¯ | ¯ ) 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 = (2/3)×(1/3) (2/3)×(1/3)+(1/3)×1 = 2 5 为什么不是这样？不太明白

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