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.

Choose the correct answer in each of the following:

Let us firstly assume, A_{1} denote the events that a red ball is transferred from bag I to II

And, A_{2} denote the event that a black ball is transferred from bag I to II

∴

And,

Let X be the event that the drawn ball is red

∴ when red ball is transferred from bag I to II,

And, when black ball is transferred from bag I to II,

Hence,

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