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Hypergeometric Distribution PMF Calculator

P(X = k) = C(K,k) · C(N−K,n−k) / C(N,n).

Compute the hypergeometric PMF P(X = k) for sampling n items without replacement from a population of N containing K successes — for example, the probability of drawing exactly k aces in a 5-card hand from a 52-card deck.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

P(X = k) = C(K, k) · C(N − K, n − k) / C(N, n)

In depth

Compute the hypergeometric PMF P(X = k) for sampling n items without replacement from a population of N containing K successes — for example, the probability of drawing exactly k aces in a 5-card hand from a 52-card deck.