1. Verify the transition in (7) and that the resulting expression is indeed the desired result.
2. Consider the following game of chance. Two fair dice are rolled repeat- edly and independently. If the sum of the outcomes is either 7 or 11, the player wins immediately, while if the sum is either 2 or 3 or 12, the player loses immediately. If the sum is either 4 or 5 or 6 or 8 or 9 or 10, the player continues rolling the dice until either the same sum appears before a sum of 7 appears in which case he wins, or until a sum of 7 appears before the original sum appears in which case the player loses. It is assumed that the game terminates the ?rst time the player wins or loses. What is the probability of winning?