🃏 Hypergeometric Distribution Calculator

What the hypergeometric distribution models

The hypergeometric distribution gives the probability of drawing a specific number of "successes" when you sample a fixed number of items without replacement from a finite population that contains a known number of successes, such as drawing a certain number of red marbles from a bag without putting any back.

How this calculator works

Enter the total population size (N), how many successes exist in that population (K), how many items you draw (n), and how many successes you want in that draw (k). The calculator applies P(X = k) = [C(K,k) × C(N-K, n-k)] / C(N,n), using combinations computed through the gamma function for accuracy with larger numbers. It also reports the cumulative probability of getting k or fewer successes, along with the expected value and variance.

Unlike the binomial distribution, the hypergeometric distribution accounts for the changing composition of the population as items are removed. This tool is intended for general statistics education and problem solving.