Solution
Seven Before Eight
Show the problem again
Two fair dice are rolled repeatedly. What is the probability that a sum of 7 appears before a sum of 8? Express as a fraction.
Worked solution
The answer is 6/11. Rolls that are neither 7 nor 8 are irrelevant; condition on the first roll that is one of them. There are 6 ways to roll a 7 and 5 ways to roll an 8, so P(7 first) = 6/(6+5) = 6/11. This "race" conditioning trick underlies the analysis of craps.
Source: Standard craps-style race-between-sums exercise from probability texts. Statement written for AxiomIQ.