You play the following simple game of chance. A fair coin is flipped. If it comes up heads, you win a dollar. If it comes up tails, you lose a dollar. Suppose you start with N dollars in your pocket. You play repeatedly until you either reach M dollars or lose all your money, whichever comes first. M and N are fixed positive integers such that 0 < N < M. 1. Show that with probability one the game ends, in other words, that the amount of money in your pocket will eventually hit 0 or M. 2. What is the probability that the game ends with M dollars in your pocket