[题目]甲.乙两门高射炮同时向一敌机开炮.已知甲击中敌机的概率为0.6.乙击中敌机的概率为0.8.敌机被击中的概率为．题目和参考答案——青夏教育精英家教网—

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【题目】甲、乙两门高射炮同时向一敌机开炮，已知甲击中敌机的概率为0.6，乙击中敌机的概率为0.8，敌机被击中的概率为________．

【答案】0.92

【解析】解法一：设“甲击中敌机”为事件A，“乙击中敌机”为事件B，事件A、B相互独立，所以所求的概率为P＝P(A∩B)＋P(∩B)＋P(A∩)＝P(A)·P(B)＋P()·P(B)＋P(A)·P()＝0.6×0.8＋0.4×0.8＋0.6×0.2＝0.92.

解法二：利用对立事件的概率，P＝1－P(∩)＝1－P()·P()＝1－(1－0.6)(1－0.8)＝0.92.

解法三：敌机被击中为事件A∪B，P(A∪B)＝P(A)＋P(B)－P(A∩B)＝P(A)＋P(B)－P(A)·P(B)＝0.6＋0.8－0.6×0.8＝0.92.

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