Editing Probabilistic method (section)

{{short description|Nonconstructive method for mathematical proofs}}

In [[mathematics]], the '''probabilistic method''' is a [[nonconstructive proof|nonconstructive]] method, primarily used in [[combinatorics]] and pioneered by [[Paul Erdős]], for [[mathematical proof|proving]] the existence of a prescribed kind of mathematical object. It works by showing that if one randomly chooses objects from a specified class, the [[probability]] that the result is of the prescribed kind is strictly greater than zero. Although the proof uses probability, the final conclusion is determined for ''certain'', without any possible error.

This method has now been applied to other areas of [[mathematics]] such as [[number theory]], [[linear algebra]], and [[real analysis]], as well as in [[computer science]] (e.g. [[randomized rounding]]), and [[information theory]].