Question

概率问题 设事件A与B相互独立,已知P(A)=0.4,P(AUB)=0.7,试求P(B|A)

Answer 1

A和B相互独立，所以P(B|A)=P(AB)/P(A)=P(A)P(B)/P(A)=P(B)
P(AUB)=P(A)+P(B)-P(AB)=0.4+P(B)-P(A)P(B)=0.4+(1-0.4)P(B)=0.4+0.6P(B)=0.7
所以P(B)=0.5
所以P(B|A)=0.5

Answer 2

A和B相互独立，所以P(B|A)=P(AB)/P(A)=P(A)P(B)/P(A)=P(B)
P(AUB)=P(A)+P(B)=0.7
所以P(B)=0.3
所以P(B|A)=0.3

Answer 3

P(A)=0.4,P(AUB)=P(A)+P(B)=0.7
∴P(B)=0.3 P(AB)=0.12
P(A|B)=P(A)-P(AB)=0.4-.12=0.28