\begin{definition}[Definition:Independent Events/Definition 2]
Let $\EE$ be an experiment with probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $A, B \in \Sigma$ be events of $\EE$ such that $\map \Pr A > 0$ and $\map \Pr B > 0$.
The events $A$ and $B$ are defined as '''independent (of each other)''' {{iff}} the occurrence of both of them together has the same probability as the product of the probabilities of each of them occurring on their own.
Formally, $A$ and $B$ are independent {{iff}}:
:$\map \Pr {A \cap B} = \map \Pr A \map \Pr B$
\end{definition}