hypergeometric distribution

Setting:

• draw from an urn with \(N\) total balls
• there are \(K\) blue balls and \(N-K\) red balls
• if you make \(n\) draws without replacement, what is the probability of getting exactly \(k\) blue balls?

PMF: \[ p_X(k) = \frac{\binom{K}{k}\binom{N-K}{n-k}}{\binom{N}{n}} \]

• see fisher exact test note for derivation