Bernoulli's Theorem

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.