Hypergeometric Distribution
A discrete random variable follows the Hypergeometric distribution if it represents the number of successes in a sample of size drawn without replacement from a finite population of items that contains successes. Formally, the Hypergeometric distribution of a random variable is given by the probability mass function,
where is the number of successes in the sample and satisfies .
Intuition
We want to draw balls from a box of balls without replacement. Consider a case of a sequence of n draws where the first balls are black and the next balls are white. Then, the probability of this particular sequence will be:
Because of this, each sample point of a Hypergeometric distribution can be viewed as binomial without repetition.
Now, in order to find all distinct sequences with draws of black balls and white balls, we need to multiply by , leading to:
If we had white, black and orange balls, then we need another variable, say , for the number of draws of white balls, and the rest would go to orange.