1. The problem statement, all variables and given/known data You decide to play monthly in two different lotteries, and you stop playing as soon as you win a prize in one (or both) lotteries of at least one million euros. Suppose that every time you participate in these lotteries, the probability to win one million (or more) euros is p1 for one of the lotteries and p2 for the other. Let M be the number of times you participate in these lotteries until winning at least one prize. What kind of distribution does M have, and what is its parameter? 2. Relevant equations Binomial Distribution: bin(n, p) px(k) = p(X = K) = (n choose k) * p^k * (1 -p)^(N-k) for k = 0, 1, ..., n Gemetric distribution: Geo(p): Px(k) = P(X = k) = (1-p)^(k-1)p for k = 1, 2, ... 3. The attempt at a solution I'm pretty sure this is a geometric distribution. However, I'm not quite sure what the p is. I think it's p1 * (1 - p2) + p2 * (1 - p1) + p1 * p2 = p1 + p2 - p1p2 so would the parameter be (p1 + p2 - p1p2)?