Definition:Event/Occurrence/Symmetric Difference
< Definition:Event | Occurrence(Redirected from Definition:Symmetric Difference of Events)
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Definition
Let the probability space of an experiment $\EE$ be $\struct {\Omega, \Sigma, \Pr}$.
Let $A, B \in \Sigma$ be events, so that $A \subseteq \Omega$ and $B \subseteq \Omega$.
Let the outcome of the experiment be $\omega \in \Omega$.
Let $\omega \in A \symdif B$, where $A \symdif B$ denotes the symmetric difference of $A$ and $B$.
Then either $A$ occurs or $B$ occurs, but not both.