题目内容
甲射击命中目标的概率是
,乙命中目标的概率是
,丙命中目标的概率是
.现在三人同时射击目标,则目标被击中的概率为( ).
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034830157338.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034830172327.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034830188303.png)
A.![]() | B.![]() | C.![]() | D.![]() |
A
设甲命中目标为事件A,乙命中目标为事件B,丙命中目标为事件C,击中目标表示事件A,B,C中至少有一个发生.∵P(
)=P(
)·P(
)·P(
)=[1-P(A)]·[1-P(B)]·[1-P(C)]=
=
.
∴目标被击中的概率为1-P(
)=1-
=
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034830266489.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034830281304.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034830297312.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034830297318.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240348303281073.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034830188303.png)
∴目标被击中的概率为1-P(
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034830266489.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034830188303.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034830203385.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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