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Assume that a gambler plays a fair game where he can win or lose 1 dollar in each round . His initial stock is 200 dollar. He decides a priory to stop gambling at the moment when he either has 500 dollars or 0 dollars in his stock. Time is counted by the number of rounds played.

i) show that the probability that he will never stops gambling is zero

ii ) Compute the probability that at the time when he stops gambling he has 500 dollars and the probability that he has zero dollars