You've calculated the probability that _some_ individual will be assaulted. The probability that a given female will be assaulted though would be (I think): P

You've calculated the probability that _some_ individual will be assaulted. The probability that a given female will be assaulted though would be (I think): P = 1 - \sum_{m=0}^K \choose{m}{K} (1-beta)^m (1-alpha)^m alpha^{K-m}