A box A contains 2 white, 3 red and 2 black balls. Another box B contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box B is?

For the bag A we can see that there are 2 white, 3 red and 2 black balls. Similarly, from bag B we have 4 white, 2 red and 3 black balls.
Probability of choosing a white and then a red ball from bag B is given by=
(4C1 × 2C1)/9C2
Probability of choosing a white ball then a red ball from bag A is given by=
(2C1 × 3C1)/7C2
So, the probability of getting a white ball and then a red ball from bag B is given by
[(4C1 × 2C1)/9C2] / [(4C1 × 2C1)/9C2 + (2C1 × 3C1)/7C2] = 8/36 / (8/36 + 6/21) = 8/36 / (8/36 + 2/7) = (8/36) / [(56 + 72)/252] = (8/36) / (128/252) = (8/36) × (252/128) = 7/16