1. The problem statement, all variables and given/known data In playing a certain game, your ability scores are determined by six independent rolls of three dice. After each set of six rolls, you are given the choice of keeping your scores or starting over. (a) How many times should you expect to start over in order to get a set of ability scores with at least two scores that are 18? 2. Relevant equations Binomial Probability Formula = (N choose K)Pkqn-k E(X)=1/p From the PGF for Geometric Distribution 3. The attempt at a solution Probability of rolling three sixes (18) is 1/216. P(Rolling 18 ≥ 2 in 6 trials) = 1 - P(0 18s) - P(1 18) = 1 - (215/216)6 - (6)(1/216)(215/216)5 ≈ .00031755 (Binomial Probability Formula) Using the Geometric (.00031755) Distribution, E(X) = 1/p = 1/.00031755 ≈ 3149 Where E(X) is the expected number of repeats before getting ≥ 2 18s.