Consider two classes, A and B, playing "coin toss" until one of the classes wins n games. Assume that the probability of A, tossing coin "head" is the same for each game and equal to p, and the probability of A tossing coin "tail" is 1-p. (Hence, there are no ties.) Let P(i,j) be the probability of A winning the series if A needs i more coin tosses to win the series and B needs j more coin tosses to win the series. Set up a recurrence relation for P(ij) that can be used by a dynamic programming algorithm. P(ij) = p P(i-1.j-1) + (1-p) P(i-1.j-1) P(ij) (1-p) P(i-1.j) + p P(ij-1) P(ij) p P(i-1.j) + (1-p) P(i.j-1) P(i+1j+1)= p P(i-1.j) + (1-p) P(ij-1) P(i+1j+1) = p P(ij) + (1-p) P(ij)

Consider two classes, A and B, playing "coin toss" until one of the classes wins n games. Assume that the probability of A, tossing coin "head" is the same for each game and equal to p, and the probability of A tossing coin "tail" is 1-p. (Hence, there are no ties.) Let P(i,j) be the probability of A winning the series if A needs i more coin tosses to win the series and B needs j more coin tosses to win the series. Set up a recurrence relation for P(ij) that can be used by a dynamic programming algorithm. P(ij) = p P(i-1.j-1) + (1-p) P(i-1.j-1) P(ij) (1-p) P(i-1.j) + p P(ij-1) P(ij) p P(i-1.j) + (1-p) P(i.j-1) P(i+1j+1)= p P(i-1.j) + (1-p) P(ij-1) P(i+1j+1) = p P(ij) + (1-p) P(ij)

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter17: Markov Chains

Section: Chapter Questions

Problem 12RP

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