What is the hypergeometric distribution 🌱

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:

\[P(x \mid N, n, k) = \frac{{k \choose x} {N-k \choose n-x}}{{N \choose n}}\]
  • 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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