Two students play a game based on the total roll of two standard dice. Student A says that a 12 will be rolled first. Student B says that two consecutive 7s will be rolled first. The students keep rolling until one of them wins. What is the probability that A will win?

Let P be probability A wins from start. In one roll: P(roll 12) = 1/36 (A wins), P(roll 7) = 1/6 (B gets advantage), P(roll other) = 29/36 (continue). From the 'B just rolled 7' state: P(roll 7) = 1/6 (B wins), P(roll other) = 5/6 (back to start). Setting up the probability equation: P = (1/36) + (29/36)P + (1/6)(5/6)(P). Solving gives P = 7/13. The key is tracking the advantage state.