Question

概率论的题，求详解！

Answer 1

P(A|B)+P(~A|~B)=1
则P(A∩B)/P(B) + P(~A∩~B)/P(~B) =1
继续化简
P(A∩B)/P(B) + P(~(AUB)/P(~B) = 1
继续
P(A∩B)/P(B) + (1-P(A)-P(B)+P(A∩B))/(1-P(B)) =1
继续
P(A∩B)/P(B) + [P(A∩B)-P(A)]/(1-P(B)) =0
继续
(1-P(B))P(A∩B) + P(B)[P(A∩B)-P(A)] =0所以：P(A∩B) -P(A)P(B) =0
P(A∩B) = P(A)P(B)
那么P(B)=P(AB)/P(A)=0.5
那么
P(A∪B)=P(A)+P(B)-P(A∩B)
=0.4+0.5-0.2
=0.7