# The Law of the Large Numbers > [!tip] Strong Law > > $ > P(\bar X_n \to \mu) = 1 > $ > [!tip] Weak Law > > For all $\epsilon > 0$, $P(|\bar X_n - \mu| > \epsilon) \to 0$ as > $n \to \infty$. > > This is the _convergence in probability_. Every time we perform simulations, we are assuming LLN implicitly. To understand this concept, consider the proportion of heads in a series of coin tosses. - SLLN suggests that $\bar X_1$, $\bar X_2$, ... crystallizes into ==a sequence which converge to $1/2$==. - WLLN suggests that for $P(\bar X_n > 1/2)$ ==can be made as close to $0$ as possible by increasing $n$==. The distribution of $\bar X_n$ along the way of becoming a constant is given by [[clt|Central Limit Theorem]]. [[recurrence]]