A bag X contains 4 white balls and 2 black balls, while another bag Y contains 3 white balls and 3 black balls. Two balls are drawn (without replacement ) at random from one of the bags and were found to be white and one black. Find the probability that the balls were drawn from bag Y.
Let A be the events of drawing one white and one black ball from any one of the bag without replacement.
and be the events of drawing bag X and Y resp. Then
and
By Bayes theorem,