Definition:Independent Events/Definition 2
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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 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 if and only if:
- $\map \Pr {A \cap B} = \map \Pr A \map \Pr B$
Also see
Sources
- 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $\S 1.7$: Independent Events: $(21)$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): independence: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): independence: 1.
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): independent events