Hypergeometric distribution

The probability distribution for the number of successes in a fixed-size sample drawn without replacement from a finite population. Its probabilities depend on the population size, the number of successes in that population, and the sample size.

Probability mass function: A function assigning a probability to each possible value of a discrete random variable. The hypergeometric formula gives the probability of each possible success count.
Finite population: A population consisting of a fixed, countable number of units. The model assumes a known total population rather than an effectively unlimited source.
Binomial distribution: The distribution of successes in a fixed number of independent trials with a constant success probability. Unlike this model, the binomial distribution does not account for depletion in a finite population.
Fisher's exact test: A statistical test of association in a contingency table that computes probabilities from fixed margins. Its table probabilities are hypergeometric under the null hypothesis of independence.
Multivariate hypergeometric distribution: The joint distribution of category counts in a fixed-size sample drawn without replacement from multiple population categories. It generalizes the two-category success count to several categories sampled together.
Binomial coefficient: The number of ways to choose a fixed-size subset from a larger set, disregarding order. Combinations count favorable samples and all possible samples in its probability formula.
Simple random sample: A sample in which every subset of a given size has the same probability of selection. Each fixed-size subset is equally likely in the standard hypergeometric model.
Geometric distribution: The distribution of the number of trials until the first success in independent Bernoulli trials. It models waiting time to a success, not the count in a fixed-size sample.
Quality control: Methods for monitoring and improving whether products or processes meet specified standards. Inspection samples can estimate defect counts in finite production lots.
Exchangeability: A property of a joint probability distribution unchanged by permutations of its variables. Draw outcomes are dependent, yet their ordering is probabilistically symmetric.

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