The relative frequency of an event happening is m/n where m is the number of occurrences in n trials. If p is the probability of the event, then the relative frequency tends towards the probability as the sample size increases to infinity. Precisely, the theorem states that for any $\epsilon >0,\underset{n\to \infty }{\text{lim}}\text{Pr}\left\{\left|\frac{m}{n}-p\right|<\epsilon \right\}=1.$

This is a special case of the weak law of large numbers.