The probability of getting the white ball from A is 1/3, and the probability of catching the ball after putting it into B bag is 1/4, that is, the probability of catching the white ball added from A bag is1/3 *1/4 =1/65433.

There are 1 white balls in bag B. After adding the balls in bag A, the probability of catching this white ball is 1/4.

Then, the probability that the ball taken from the B bag is a white ball is:112+1/4 =1/3.