Events \(A\) and \(B\) are mutually exclusive (cannot both occur at once) if they have no elements in common.

Events \(A\) and \(B\) are mutually exclusive if: $$P(A∩B)=0$$

The complement of an event \(A\) in a sample space \(S\), denoted \(A^c\), is the collection of all outcomes in \(S\) that are not elements of the set \(A\). It corresponds to negating any description in words of the event \(A\).

The complement of an event \(A\) consists of all outcomes of the experiment that do not result in event \(A\).

Complement formula:

$$P(A^c)=1-P(A)$$