Definition:Independent Events/Pairwise Independent

Definition
Let $\mathcal E$ be an experiment with probability space $\left({\Omega, \Sigma, \Pr}\right)$. Let $\mathcal A = \left\{{A_i: i \in I}\right\}$ be a set of events of $\mathcal E$.

Then $\mathcal A$ is pairwise independent iff:
 * $\forall j, k \in I: \Pr \left({A_j \cap A_k}\right) = \Pr \left({A_j}\right) \Pr \left({A_k}\right)$

That is, if every pair of events of $\mathcal E$ are independent of each other.

That is, $\mathcal A$ is pairwise independent iff the condition for general independence:
 * $\displaystyle \Pr \left({\bigcap_{i \mathop \in J} A_i}\right) = \prod_{i \mathop \in J} \Pr \left({A_i}\right)$

holds whenever $\left|{J}\right| = 2$.

Also see

 * Pairwise Independence does not imply Independence: although independence (in the general sense) implies pairwise independence, a collection of events can be pairwise independent without being independent.