Box A contains 3 black balls and a white balls .Box B has 2 black balls and 3 white balls . The probability of chossing box A and B are 2/3 and 1/3 respectively . After the box is chosen , a ball is withdrawn from the box . If theball drawn is black , what is the probability that it was taken from box B ?

P(B | Bl)=P(Bl n B)/P(Bl)=(1/3 x 2/5)/(5/9)=6/25

but the answer given is 4/19 , could someone point me to my mistake ?