Definition:Independent Events/Definition 1
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Definition
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:
- $\condprob A B = \map \Pr A$
where $\condprob A B$ denotes the conditional probability of $A$ given $B$.
Also see
Sources
- 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $\S 1.7$: Independent Events: $(20)$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): independent events