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 $j \in J$ |

(ii) | $\{ E_j \}_{j \in J} \subseteq \mathcal{F}$ is an D1720: Independent event collection in $P$ |

Then $\{ E_j \}_{j \in J}$ is a D2148: Pairwise independent event collection in $P$.