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Bag A contains 3 red and 5 black balls, while bag B contains 4 red and 4 black balls. Two balls are transferred at random from bag A to bag B and then a ball is drawn from bag B at random. If the ball drawn from bag B is found to be red, find the probability that two red balls were transferred from A to B.

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Let us define the following events :

E1 = one red and one blackball is trans{erred

E2 =  two red balls are transferred

E3 =  two black balls are transferred

E = drawn ball is red.

Then,

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