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Question

Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag 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 ball is black.

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Solution

Let

Total number of balls in bag I is 7 and total number of balls in bag II is 9.

Probability of occurrence of event

Similarly, if a black ball is transferred from bag I to bag II, then probability of drawing of red ball is,

Thus, the probability that the ball transferred from bag I to bag II was black is

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