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Let U1 and U2 be two urns such that U1 c...

Let `U_1` and `U_2` be two urns such that `U_1` contains 3 white and 2 red balls, and `U_2` contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from `U_1` and put into `U_2`. However, if tail appears then 2 balls are drawn from `U_1` and put into `U_2`. Now, 1 ball is drawn at random from `U_2` Given that the drawn ball from `U_2` is white, the probability that head appeared on the coin is

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