# 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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