1. The problem statement, all variables and given/known data Roll a pair of six-sided dice. If the sum is 7 or 11, you win. If the sum is 2,3, or 12, you lose. If the sum is any other number, you roll again. In fact, you continue throwing the dice until you either roll that number again (win!) or roll a 7 (lose!). Suppose you roll a sum of 8 on the first roll. Find the probability that you subsequently win the game, given that you rolled an 8 to start with. 2. Relevant equations Conditional probability 3. The attempt at a solution I'm not sure which way is correct. First, I did: 5/36 because there are 5 ways to get a sum of 8. Then I thought about the probability being 5/11. Because there are only two outcomes that I care about. An 8 or 7. There are 5 ways to get an 8 and 6 ways to get a 7. So... 5/(5+6) = 5/11 Would someone please explain the difference between the two attempts and explain why one or the other is wrong?