设A,B是两个随机事件,P(A|B)=0.4,P(B|A)=0.4,P=0.7,则P(A+B)=_______.
设A,B是两个随机事件,P(A|B)=0.4,P(B|A)=0.4,P
=0.7,则P(A+B)=_______.
![](https://assets.51tk.com/images/854514ff373de5da_img/7ea43b5e5f3f27d8.png)
参考解析
解析:
因为P(A|B)=0.4,P(B|A)=0.4,所以P(A)=P(B)且P(AB)=0.4P(A),
解得P(A)=P(B)=
,P(AB)=
,于是P(A+B)=P(A)+P(B)-P(AB)=
![](https://assets.51tk.com/images/854514ff373de5da_img/13ad8f578cb66e30.png)
![](https://assets.51tk.com/images/854514ff373de5da_img/04328333c6abc24a.png)
![](https://assets.51tk.com/images/854514ff373de5da_img/7b2ac2bca17c7b17.png)
![](https://assets.51tk.com/images/854514ff373de5da_img/03d14d21f4744da7.png)
![](https://assets.51tk.com/images/854514ff373de5da_img/7b1cd86e7dbc7974.png)
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