Question

设AB为两个随机事件.0＜P＜1 P(A/B非）=P(A/B)证明AB相互独立

Answer 1

P(A|~B）=P(A~B）/P(~B),P(A|B）=P(AB）/P(B),得到P(A~B）/P(~B)=P(AB）/P(B),P(A~B)P(B)=P(AB)P(~B),

将P(A~B)=P(A)-P(AB),P(~B)=1-P(B)代入后即可得到P(AB)=P(A)P(B),A与B相互独立.