# With high probability

From Algorithmist

## [edit] Definition

An event occurs **with high probability** if, for any , the event occurs with probability at least , where *c*_{α} depends only on α.

Since we can choose α, we can make the probability arbitrarily low, at a cost of time and/or space.

## [edit] Example

With high probability, a set of N random numbers will contain at least Ω(N) evens.

What it means is: For any α, there exists a k (that doesn't depend on N), such that a set of N random numbers will contain at least k*N evens with probability , where *c*_{α} depends only on α.