Definition:Complementary Event

Definition
Let the probability space of an experiment $\EE$ be $\struct {\Omega, \Sigma, \Pr}$.

Let $A \in \Sigma$ be an event in $\EE$.

The complementary event to $A$ is defined as $\relcomp \Omega A$.

That is, it is the subset of the sample space of $\EE$ consisting of all the elementary events of $\EE$ that are not in $A$.