Exercise 10.41 Show that, in the Gambler’s Ruin Problem, the game terminates with probability 1. You may find it useful to partition the sequence of coin tosses into disjoint runs of length N, and to consider the event that one of these runs contains only steps to the right.

Exercise 10.42 Use Theorem 10.23 to show that, in the Gambler’s Ruin Problem, the probability that B wins the game is

μ

(a) =





(p/q)N−a − 1

( p/q)N − 1 if p 6= q,

(N − a)/N if p = q = 1 2