Definition:Independent Events/Definition 1

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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) if and only if the occurrence of one of them does not affect the probability of the occurrence of the other one.

Formally, $A$ is independent of $B$ if and only if:

$\map \Pr {A \mid B} = \map \Pr A$

where $\map \Pr {A \mid B}$ denotes the conditional probability of $A$ given $B$.

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