为什么是beyes 公式，不是条件概率吗 P(A|B)

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

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 妻子回信的概率应该是100%信件能否送达的概率是2/3这两个不应该相等

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 老师我有两个问题第一个问题是，题目明明问的是，妻子收到丈夫的信，但丈夫没收到妻子的信，妻子只有收到丈夫的信才会回信，所以第二个树杈是不存在的。为什么不是2/3*1/3=2/9？见如下图第二个问题是左红框为什么等于右红框？课程里的贝叶斯公式只有分子的推导，没有分母的推导。

NO.PZ2018122801000006 3/5 2/3 2/5 is correct. 考点 Bayes' formula 解析 (Notices: if the wife not receive the letter, she woulnot senresponse to the man.) Note: the wife receivethe letter; A ¯ : the wife not receive the letter; the mreceivea response letter from his wife; B ¯ : 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(B ¯ )   P(B ¯ )= P(A B ¯ ) P( B ¯ ) = P( B ¯ )×P( B ¯ |P( B ¯ )×P( B ¯ |A)+P( B ¯ )×P( B ¯ | A ¯ )   = (2/3)×(1/3) (2/3)×(1/3)+(1/3)×1 = 2 5   这里怎么是PAB等于PB*PB|A