# What's the difference between a binomial, hypergeometric, and Poisson probability distribution?

Binomial - Random variable $X$ is the number of successes in n independent and identical trials, where each trial has fixed probability of success.
Hypergeometric - Random variable $X$ is the number of objects that are special, among randomly selected $n$ objects from a bag that contains a total of $N$ out of which $K$ are special. If $n$ is much smaller than $N$ then this can be approximated by binomial.
Poisson - Random variable $X$ counts the number of occurrences on an event in a given period, where we know that the concurrences has an average of $\setminus \lambda$ for any period of that length, independent of any other disjoint period.