Hypergeometric Distribution Calculator

This hypergeometric distribution calculator works out the exact probability of drawing a chosen number of successes when you sample without replacement from a fixed, finite population, the situation where every draw changes the odds for the next one. You enter four numbers: the population size N, how many successes sit within that whole population K, the size of the sample you are drawing n, and the number of successes you actually want to see in that sample k. From those, the calculator returns P(X = k), the probability of getting exactly that many successes, alongside the expected number of successes for your sample size and a repeat of the k value you asked about, so you can check the result against what you set out to test. Unlike the binomial distribution, which assumes each draw is independent with a constant success probability, the hypergeometric distribution correctly accounts for the population shrinking as each item is removed, which makes it the right tool for problems like auditing a batch for defective units, working out card or lottery odds, and capture-recapture estimates in ecology. Below the calculator you will find the underlying combinatorial formula, a fully worked example you can use to check your own numbers, and the assumptions the calculation relies on, including that inputs are whole numbers within sensible limits and that the population is genuinely finite and fixed.

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