Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. Two balls are transferred at random from BSag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred balls were both black.

Given

Two balls are to be transferred at random from Bag I to Bag II.

The possibilities are as follows:

(i) 1 red and 1 black: Bag II now has 5 red and 6 black balls

(ii) 2 red and 0 black: Bag II now has 6 red and 5 black balls

(iii) 0 red and 2 black: Bag II now has 4 red and 7 black balls

We want the probability for case (iii), when both the balls transferred from Bag I to Bag II were black.

∴ The required probability of getting a red ball from Bag II in this case is