33. Two players are playing a sequence of points, which begin when one of the players serves....

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33. Two players are playing a sequence of points, which begin when one of the players serves. Suppose that player 1 wins each point she serves with probability p, and wins each point her opponent serves with probability q. Suppose the winner of a point becomes the server of the next point.

(a) Find the proportion of points that are won by player 1.

(b) Find the proportion of time that player 1 is the server.

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