Combinatorics (probability)

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 \(1\) ball which is white in colour.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 \(U_2.\)\(\mathbb{\text{What is the probability that the ball is white?.}}\)\(\mathbb{\text{The answer is of the form}}\)\(\dfrac{p}{q}\)\(\mathbb{\text{what is the value of p+q?}}\)\(\mathbb{\text{This is a JEE-2011 problem.}}\)

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