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当前位置：考试网  > 试卷库  > 学历类  > 自考  > 自考公共课  >  发报台分别以概率0.6和0.4发出信号“1”和“0”。由于通讯系统受到干扰，当发出信号“1”时，收报台未必收到信号“1”，而是分别以概率0.8和0.2收到信号“1”和“0”；同时，当发出信号“0”时，收报台分别以概率0.9和0.1收到信号“0”和“1”。求（1）收报台收到信号“1”的概率；（2）当收报台收到信号“1”时，发报台确是发出信号“1”的概率。
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发报台分别以概率0.6和0.4发出信号“1”和“0”。由于通讯系统受到干扰，当发出信号“1”时，收报台未必收到信号“1”，而是分别以概率0.8和0.2收到信号“1”和“0”；同时，当发出信号“0”时，收报台分别以概率0.9和0.1收到信号“0”和“1”。求（1）收报台收到信号“1”的概率；（2）当收报台收到信号“1”时，发报台确是发出信号“1”的概率。

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正确答案：

设A1=“发出信号1”，A0=“发出信号0”，A=“收到信号1”

(1)由全概率公式，有P(A)=P(A|A1)P(A1)+P(A|A0)P(A0)=0.8x0.6+0.1x0.4=0.52

(2)由贝叶斯公式，有P(A1|A)=P(A|A1)P(A1)/P(A)=0.8x0.6/0.52=12/13

答案解析：

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