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1. A gambler with an initial amount of k units plays a sequence of unfair games: at each time step, the gambler bets a unit and wins it back with probability p < 1/2. The gambler quits when he either becomes bankrupt or he reaches a fixed amount n.
(a) What is the probability that he becomes bankrupt?
(b) What is the expected number of steps of the game? You may assume given that the expected number of steps is bounded.

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