# Bernoulli's Theorem

(Redirected from Law of Large Numbers)

## Theorem

Let the probability of the occurrence of an event be $p$.

Let $n$ independent trials be made, with $k$ successes.

Then:

$\displaystyle \lim_{n \mathop \to \infty} \frac k n = p$

## Also presented as

This result can also be presented in the form:

$\forall \epsilon \in \R_{>0}: \displaystyle \lim_{n \mathop \to \infty} \map \Pr {\size {\frac k n - p} < \epsilon} = 1$

## Also known as

This theorem is also popularly known as the Law of Large Numbers.

## Source of Name

This entry was named for Jacob Bernoulli.