Hypergeometric Distribution Calculator

Formula and method

P(X=x) = C(K,x)C(N−K,n−x) ÷ C(N,n). The engine uses log-gamma combinations and log-sum-exp cumulative summation, avoiding floating-point factorial overflow. Feasible success bounds are derived from N, K, and n before calculation.

Worked example

For N = 50, K = 5, n = 10, and x = 1, P(X=1) is approximately 0.4313371972. P(X≤1) is approximately 0.7418999792.

Assumptions and boundaries

• Sampling is without replacement from a finite population.
• N, K, n, and success counts are integers within their feasible bounds.
• Population size is limited to 1,000,000 and sample size to 10,000 for responsive local computation.
• Binomial Distribution Calculator instead models independent trials with a constant success probability.

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