Probability that the gambler quits a winner

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1. Suppose that on each play of the game a gambler either wins 1 with probability p or loses 1 with probability 1 - p. The gambler continues betting until she or he is either up n or down m. What is the probability that the gambler quits a winner?

2. A particle moves among n + 1 vertices that are situated on a circle in the following manner. At each step it moves one step either in the clockwise direction with prob- ability p or the counterclockwise direction with probability q = 1 - p. Starting at a speci?ed state, call it state 0, let T be the time of the ?rst return to state 0. Find the probability that all states have been visited by time T.

Reference no: EM131005760

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