25. A gambler wins each game with probability p. In each of the following cases, determine the...

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25. A gambler wins each game with probability p. In each of the following cases, determine the expected total number of wins.

(a) The gambler will play n games; if he wins X of these games, then he will play an additional X games before stopping.

(b) The gambler will play until he wins; if it takes him Y games to get this win, then he will play an additional Y games.

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