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A gambler repeatedly plays a game for which his probabilities of winning a dollar is p and of losing a dollar is (1 p) each

  1. A gambler repeatedly plays a game for which his probabilities of winning a dollar is p and of losing a dollar is (1 p) each time he plays. The games are independent. He plans to play the game repeatedly until he is ruined (loses all his money) or has 3 dollars. If the gambler begins with 1 dollar, what is the probability that he is ruined?

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