# With high probability

From Algorithmist

Revision as of 07:46, 3 April 2014 by 134.61.167.138 (Talk) (O as lower bound makes no sense. Omega is needed here.)

## Definition

An event occurs **with high probability** if, for any , the event occurs with probability at least , where depends only on .

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

## Example

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

What it means is: For any , 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 depends only on .