Definition:Independent Events/Definition 2
Jump to navigation
Jump to search
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: $(21)$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): independent events