Mutually exclusive

Probability

In probability theory, events E₁, E₂, ..., E_n are said to be mutually exclusive if the occurrence of any one of them implies the non-occurrence of the remaining n − 1 events. Therefore, two mutually exclusive events cannot both occur. Formally said, ${\displaystyle X}$ is a set of mutually exclusive events if and only if given any ${\displaystyle E_{i},E_{j}\in X}$, if ${\displaystyle E_{i}\neq E_{j}}$ then ${\displaystyle E_{i}\cap E_{j}=\varnothing }$. As a consequence, mutually exclusive events have the property: ${\displaystyle P(A\cap B)=0}$.