In the gambler's ruin problem of Section 4.5.1, suppose the gambler's fortune is presently i, and suppose that we know that the gambler's fortune will eventually reach N (before it goes to 0). Given this information, show that the probability he wins the next gamble is P[1-(q/p)+] 1- (q/p) i+1 2i if p if p = Hint: The probability we want is PX+1 +1|X = i, lim xm = N] P(X+1=i+1, lim, X = N|X = i) Pilim, X, NIX, = i =