Probabilistic Method

This article is not about interactive proof systems which use probability to convince a verifier that a proof is correct, nor about probabilistic algorithms, which give the right answer with high probability but not with certainty, nor about Monte Carlo methods, which are simulations relying on pseudo-randomness.The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for 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 more than zero.
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