1. Problem 9.33 An absent-minded professor has m matches in his right pocket and m matches in his left pocket. Each time he needs a match, he reaches for a match in his left pocket with probability p and in his right pocket with probability 1 − p. When the professor first discovers that one of his pockets is empty, what is the probability that the other pocket has exactly k matches for k =0,1,...,m? This problem is known as the Banach match problem.