Statistics Calculators

Hypergeometric Distribution Calculator

Calculate the probability of drawing a specific number of successes from a finite population without replacement.

P(X = k) —

Mean (expected successes) —

Variance —

About the Hypergeometric Distribution Calculator

The hypergeometric distribution finds the probability of a specific number of successes when drawing a sample from a finite population without replacement — such as drawing winning cards from a deck or defective parts from a batch.

Formula: P(X = k) = [C(K, k) × C(N − K, n − k)] ÷ C(N, n)

Because each draw changes the composition of what's left, this differs from the binomial distribution, which assumes replacement (or an effectively infinite population) so that each trial's probability stays constant.