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(i,j) that can be used by a dynamic programming algorithm. P(i+1,j+1)=pP(i,j)+(1p)P(i,j)P(i,j)=pP(i1,j)+(1p)P(i,j1)P(i,j)=(1p)P(i1,j)+pP(i,j1)P(i+1,j+1)=pP(i1,j)+(1p)P(i,j1)P(i,j)=pP(i1,j1)+(1p)P(i1,j1)