Hypergeometric Distribution Calculator
Calculate probabilities for sampling without replacement using the hypergeometric distribution. Find the exact probability of drawing a specific number of success items from a finite population.
The hypergeometric distribution models the number of successes in n draws from a finite population of N items containing K successes, without replacement. Unlike the binomial distribution, each draw changes the probability of the next.
Formula: P(X = k) = C(K, k) x C(N-K, n-k) / C(N, n), where C(a, b) is the binomial coefficient. The key properties are: E(X) = nK/N and Var(X) = n(K/N)((N-K)/N)((N-n)/(N-1)). The factor (N-n)/(N-1) is called the finite population correction.
Classic examples: Drawing cards from a deck (what is the probability of getting exactly 3 hearts in a 5-card hand?), quality control (testing a batch of products without replacement), ecology (capture-recapture methods for estimating population sizes), and lottery calculations where order does not matter.