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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 at random from $$U_1$$ and put into $$U_2$$. Now 1 ball is drawn at random from $$U_2$$.
Question 62
Given that the drawn ball from $$U_2$$ is white, the probability that head appeared on the coin is
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