Question

设P(A)=1/4,P(B/A)=1/3,P(A/B)=1/2,则P(A B)=

Answer 1

P(B|A) =1/3

P(A∩B)/P(A) =1/3

P(A∩B) =(1/3)(1/4) =1/12

P(A|B) =1/2

P(A∩B)/P(B) =1/2

P(B) = (1/12)/(1/2) = 1/6

P(AUB) =P(A)+P(B) -P(A∩B)

=1/4+1/6 - 1/12

= 1/3