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 1p. (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(i,j) that can be used by a dynamic programming algorithm.

A-) P(i,j) = p P(i-1,j) + (1-p) P(i,j-1)

B-) P(i+1,j+1) = p P(i,j) + (1-p) P(i,j)

C-) P(i,j) = (1-p) P(i-1,j) + p P(i,j-1)

D-) P(i+1,j+1) = p P(i-1,j) + (1-p) P(i,j-1)

E-) P(i,j) = p P(i-1,j-1) + (1-p) P(i-1,j-1)