[SOLVED] Probability of Rolling a 5 or 7 1. The problem statement, all variables and given/known data A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probability that a 5 occurs first. 2. Relevant equations Axioms and basic theorems of probability. 3. The attempt at a solution There are 36 possible outcomes of a roll of a pair of dice, 4 of which result in a sum of 5 and 6 of which result in a sum of 7. Let A be event of rolling a 5 and B of rolling a 7. Then P(A) = 4/36 and P(B) = 6/36. The probability of rolling a 5 or 7 is P(A or B) = P(A) + P(B) = 10/36. The probability of not rolling a 5 or 7 is thus 1 - 10/36 = 26/36. Define E(n) as the event that the nth roll results in a 5 and let p(n) be it's probability. If the nth roll resulted in a 5, then there were no previous rolls resulting in 5 or 7, so p(n) is thus equal to (26/36)^(n - 1) * 4/36. The probability sought then is just the sum of p(n) for all legal values of n, which is an infinite sum. Is this right? I don't know what the sum is but it must definitely be less than or equal to 4/36.