Q. 28

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.

Answer :


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

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