What is the hypergeometric distribution 🌱

Last updated on March 13, 2021

Suppose a population consists of $N$ items, $k$ of which are successes. And a random sample drawn from that population consists of $n$ items, $x$ of which are successes. Then the hypergeometric probability is:

P (x ∣ N, n, k) = \frac{(\binom{k}{x}) (\binom{N - k}{n - x})}{(\binom{N}{n})}

The number of combinations between:
- Ways to choose x successes from k successes
- Ways to choose n-x successes from N-k successes
Divided by number of ways to choose n samples from N total items

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