Hypergeometric Distribution Calculator
Calculate the probability of k successes in n draws without replacement.
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Enter the population size (N), the number of success items in the population (K), the sample size (n), and the number of desired successes (k). The calculator computes the exact probability using the hypergeometric formula: C(K,k)*C(N-K,n-k)/C(N,n).
About This Calculator
The hypergeometric distribution models drawing without replacement from a finite population. Unlike the binomial distribution, which assumes replacement (or an infinite population), the hypergeometric accounts for the changing composition as items are drawn. Classic example: drawing cards from a deck.
Frequently Asked Questions
When should I use hypergeometric instead of binomial?
Use hypergeometric when sampling without replacement from a finite population. If the population is much larger than the sample (at least 20x), the binomial is a good approximation.
What is a real-world example?
Drawing 5 cards from a 52-card deck and wanting exactly 2 hearts. N=52, K=13, n=5, k=2.
What is the mean of the hypergeometric distribution?
The mean is n*K/N. For drawing 5 cards and counting hearts: 5*13/52 = 1.25 hearts expected.