Plya's Urn Problem:

Initially there is 1 red and 1 blue ball in an urn. In each step, we select a ball from the urn uniformly at random, and then put it back together with a new ball of the same color. Therefore after n steps, there are n + 2 balls in the urn. Suppose that after n steps there are r + 1 red and b + 1 blue balls, where r + b = n. Show that r/(r + b) is the conditional probability that a red ball was selected in the first step. Fully justify your answer.

Hint: Let C1 be the color of the first ball selected. Let Rn the number of red balls after n steps. Explain why

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