Question

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 one white and one black. Find the probability that the balls were drawn from bag Y.

Answer 1

Let  E₁ and E₂ be the events of drawing bag X and bag Y respectively.

Then   P(E₁) = P(E₂) = 1/2

Let A be the event of drawing one white and one black ball from any one of the bag without replacement. Then,