>>11388453Say the events are independent and the probability of a single one of those events happening is p. Then the probability of that event not happening is 1 - p. You can split the problem up by considering the probability the event happens once, twice, ...., X times separately then adding them. The probability the event occurs k times is C(n, k)p^k(1 - p)^(n - k) because it doesn't occur n - k times, and there are C(n, k) possible ways k events can occur in X attempts. Adding, this up you get
substitute in 1/N and you get 1 - (1 - 1/N)^X.
