设事件A, B满足 0<P(A)<1, 0<P(B)<1, P(A|B) ≥ P( A| B的逆)

Question

设事件A, B满足 0<P(A)<1, 0<P(B)<1, P(A|B) ≥ P( A| B的逆)原题看图片，我搞不懂为什么P(B)大于P(B|A的逆)

Answer 1

楼主您好
P(B|A)>=P(B) => P(AB)>=P(A)P(B) => P(B)-P(AB)<=P(B)-P(A)P(B) => P(BA非)<=P(B)(1-P(A)) => P(BA非)<=P(B)P(A非) => P(B)>=P(BA非)/P(A非) => P(B)>=P(B|A非)
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