Weak Law of Large Numbers

Theorem

The Average of Independent RVs converges to their common mean $\mu$ $P(|{\overline{X}}_n-\mu |\ge ϵ)\to 0\text{ as }n\to \infty ,\forall ϵ>0$

Intuition

We want to say the difference between out sample mean from the theoretical mean to be within $ϵ$, so the odds that they are outside will approach 0 as the number of trials increases to infinity.