> [!NOTE] Definition (Mutual Independence) > Let $(\Omega, \mathcal{F}, \mathbb{P})$ be a [[Probability Space|probability space]]. Let $n\in \mathbb{N}^{+}$ and $A_{1},A_{2},A_{3},\dots A_{n} \in \mathcal{F}$. The events $A_{1},A_{2},\dots, A_{n}$ are *mutually independent* iff for all $J \subset \{ 1,\dots, n \}$ $\mathbb{P}\left( \bigcap_{i\in J} A_{i} \right) = \prod_{i\in J} \mathbb{P}(A_{i}) $