Definition:Independent Events/Pairwise Independent

Definition
Let $\EE$ be an experiment with probability space $\struct {\Omega, \Sigma, \Pr}$. Let $\AA = \family {A_i}_{i \mathop \in I}$ be an indexed family of events of $\EE$.

Then $\AA$ is pairwise independent :
 * $\forall j, k \in I: \map \Pr {A_j \cap A_k} = \map \Pr {A_j} \map \Pr {A_k}$

That is, every pair of events of $\EE$ are independent of each other.

That is, $\AA$ is pairwise independent the condition for general independence:
 * $\ds \map \Pr {\bigcap_{i \mathop \in J} A_i} = \prod_{i \mathop \in J} \map \Pr {A_i}$

holds whenever $\card J = 2$.

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.