Consider the gambler’s ruin problem, with the exception that A and B agree to play no more than games. Let P_n,i denote the probability that A winds up with all the money when starts with i and B starts with N - i. Derive an equation for P_n,i in terms of P_n-1,i+1 and P_n-1,i-1 and compute P_7,3, N = 5.