The hypergeometric distribution is a discrete probability distribution that describes the probability of obtaining a certain number of successes in a sample drawn without replacement from a finite population. Unlike the binomial distribution, where the probability of success remains constant, the hypergeometric distribution accounts for the changing probabilities as items are drawn from the population.

To apply the hypergeometric distribution, you need four key parameters: the total number of items in the population (N), the total number of desired items in that population (K), the number of draws (n), and the number of desired items in your sample (k). For example, if you want to find the probability of drawing a specific number of kings from a deck of cards, you would use these parameters to compute the probability mass function (PMF) ¹².

This distribution is particularly useful in scenarios such as card games, lottery systems, or any situation where sampling occurs without replacement, making it a valuable tool in data science and statistics.