A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.

The Poisson distribution may be used to approximate the binomial if the probability of success is "small" (such as 0.01) and the number of trials is "large" (such as 1,000).

This text is adapted from Openstax, Introductory Statistics, Section 4.6