Definition:Event/Occurrence/Symmetric Difference

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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.


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