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An investor has at time t = 0 a dollar amount of S_0 = a > 1, with a an integer. Each day they gain

An investor has at time t = 0 a dollar amount of S_0 = a > 1, with a an integer. Each day they gain or lose 1 dollar with probability 1/2 . Find the probabilty that at some point during the interval of time {1, . . . , n} the investor has no dollars.

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