一道数学题

我是魔鬼

Each document has both a paper copy and an electrical copy. Of the paper copies that are inaccurate, 60% also has an inaccurate electrical copies. Of the electrical copies that are inaccurate, 75% also has an inaccurate paper copy. 3% of documents has both inaccurate paper copy and electric copy. What's the probability a randomly drawn document has both accurate paper and accurate electrical copy?

mikejia

这就是条件概率的公式，概率论里的。

E 发生的情况下P再发生的概率。

sammen

根据条件概率公式：P(P|E)=P(EP)/P(E)，这个公式是哪里来的啊？请问。

himba

记E为事件Electrical copy错误,P为Paper copy错误

由题意知：P(P|E)=75%, P(E|P)=60% P(EP)=3%

根据条件概率公式：P(P|E)=P(EP)/P(E)

所以P(E)=P(EP)/P(P|E)=3%/75%=4%

同理可得P(P)=5%

所以P(E+P)=P(P)+P(E)-P(EP)=6%

所以Both accurate的probability=1-6%=94%