(1) A theorem in probability theory that describes the behavior of the frequency of occurrence of some event in a sequence of independent trials. It is a special case of the law of large numbers.
(2) One of the limit theorems in probability theory. It permits an approximate estimate to be made of the probability of a given number of occurrences of an unlikely event in a large number of independent trials.
Both theorems were proved by S. D. Poisson in 1837.