Hypergeometric Distribution Calculator
Calculate exact successes in a sample drawn without replacement.
How the hypergeometric distribution calculator works
The hypergeometric distribution counts successes in a finite sample drawn without replacement, so each draw changes the remaining composition. Exactly k successes can be chosen from the population’s K successes while the remaining sample positions come from failures. Multiplying those combination counts and dividing by all size-n samples yields the exact probability without an independence approximation.
The defaults describe 20 items containing 7 successes, with 5 drawn and exactly 2 successes observed. Favorable samples number 7 choose 2 times 13 choose 3, or 6006, while all samples number 20 choose 5, or 15504. The verified exact probability is 6006 divided by 15504, approximately 0.3873839009.
Reading hypergeometric distribution calculator results privately
Sampling must be uniformly random without replacement from a finite population whose success count is known. Impossible observed values naturally produce probability zero through the combination terms. Large populations can exceed precise floating-point combination counts; this page is aimed at moderate classroom and planning examples rather than arbitrary-precision combinatorics. This hypergeometric distribution calculator calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
How is hypergeometric different from binomial?
Hypergeometric sampling is without replacement, so draws are dependent. Binomial trials use a constant success probability with independence.
What is the expected number of successes?
It is sample size times the population success proportion, n times K divided by N.
Is the hypergeometric distribution calculator private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
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