Intuitively it might make sense to add the probabilities, but it doesn't actually work out that way[0]. The parent used the law of total probability to solve fo

Intuitively it might make sense to add the probabilities, but it doesn't actually work out that way[0]. The parent used the law of total probability to solve for the probability of hitting at least once because it's simpler: P(hits >= 1) = 1 - P(hits = 0). Solving for the left side of the equation directly gets trickier: P(hits >= 1) = P(hits = 1) + P(hits = 2) + ... + P(hits = k) P(hits = 1) = 100 chose 1 * 0.01^1 * 0.99^99 ... p(hits = n) = 100 chose n * 0.01^n *0.99^(100-n) Taking that sum where n=100 yields the same as 1 - P(hits = 0) = 1 - (100 chose 0 *0.1^0 *0.99^100) = 1 - 0.99^100 [0] https://en.wikipedia.org/wiki/Binomial_distribution https://en.wikipedia.org/wiki/Binomial_distribution