Please provide detailed explanation. Thank you.

19. Consider the gambler's ruin problem, with the excep tion that A and B agree to play no more than n games. Let Pny denote the probability that A winds up with all the money when A starts with i and B starts with N - i. Derive 23. an equation for Pn,; in terms of Pn-1. it1 and P-1. i-1, and sen compute P7,3, N = 5