Unlock: Hypergeometric Distribution

The Hypergeometric distribution is the law of the success count in n draws without replacement from a finite population of N items, K of which are successes. The PMF is the ratio of three binomial coefficients. The mean is nK/N, identical to the Binomial with p = K/N, but the variance carries the finite-population correction (N-n)/(N-1). The Binomial is the n << N limit. Fisher's exact test, capture-recapture, and quality-control acceptance sampling read off the Hypergeometric directly.