Hypergeometric Distribution Calculator

Probability of drawing successes without replacement

Total number of items in the population.
Number of items in the population that are considered successes.
Number of items drawn from the population (without replacement).
The exact number of successes you want to find the probability for.

Results

P(X = k) - Exactly k successes
P(X <= k) - CDF
P(X > k)
P(X >= 1) - At least one
Expected Value E(X)
Variance Var(X)
Std Deviation

Full Distribution

Distribution Table

kP(X=k)P(X<=k)
PMF: P(X=k) = C(K,k)*C(N-K,n-k) / C(N,n)
E(X): n*K/N
Var(X): n*K*(N-K)*(N-n) / (N^2*(N-1))
Method: Uses log-gamma for stable computation of large binomial coefficients.