From a population of size N, containing a subpopulation of size m, a sample of size n is drawn at random without replacement. The number, X, of the sample that were drawn from the subpopulation is said to have a Hypergeometric distribution, H(N,m,n).

The exact probability is calculated. For example, P( X<= 75|1600,400,300) = .53252.

Computation time is proportional to x+min(m,n,N-m,N-n).