Definition:Independent Events/Definition 2

Definition
Let $\mathcal E$ be an experiment with probability space $\left({\Omega, \Sigma, \Pr}\right)$.

Let $A, B \in \Sigma$ be events of $\mathcal E$ such that $\Pr \left({A}\right) > 0$ and $\Pr \left({B}\right) > 0$.

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:
 * $\Pr \left({A \cap B}\right) = \Pr \left({A}\right) \Pr \left({B}\right)$

Also see

 * Equivalence of Definitions of Independent Events