A gambler repeatedly bets that a die will come up 6 when
Chapter 9, Problem 23E(choose chapter or problem)
Problem 23E
A gambler repeatedly bets that a die will come up 6 when rolled. Each time the die comes up 6, the gambler wins $1; each time it does not, the gambler loses $1. He will quit playing either when he is ruined or when he wins $300. If Pn is the probability that the gambler is ruined when he begins play with $n, then for all integers k with 2 ≤ k ≤ 300. Also P0 = 1 and P300 = 0. Find an explicit formula for Pn and use it to calculate P20. (Exercise 33 in Section 9.9 asks you to derive the recurrence relation.)
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