Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$E_j \in \mathcal{F}$ is an D1716: Event in $P$ for each $j \in J$

Then $E = \{ E_j \}_{j \in J}$ is a pairwise independent collection of events in $P$ if and only if \begin{equation} \forall \, i, j \in J \, (i \neq j \quad \implies \quad \mathbb{P}(E_i \cap E_j) = \mathbb{P}(E_i) \mathbb{P}(E_j)) \end{equation}