Monte Carlo simulation empirically demonstrates fundamental probability theorems: The Weak Law of Large Numbers \(\lim_{n \to \infty} P(|\bar{X}_n - \mu| \ge \epsilon) = 0\), the Central Limit Theorem stating sums of i.i.d. random variables converge to Gaussian \(\mathcal{N}(n\mu, n\sigma^2)\), Binomial distribution \(P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}\), and the Birthday Collision Theorem \(P(\ge 1 \text{ match}) = 1 - \prod_{i=1}^{n-1}(1 - i/365)\).