\begin{definition}[Definition:Independent Events/Pairwise Independent]
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''' {{iff}}:
:$\forall j, k \in I: \map \Pr {A_j \cap A_k} = \map \Pr {A_j} \map \Pr {A_k}$
That is, {{iff}} every pair of events of $\EE$ are independent of each other.
That is, $\AA$ is '''pairwise independent''' {{iff}} 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 $\card J = 2$.
\end{definition}