# A die is rolled.Let E be the event "die shows 4" anf F be the event "die shows even number".Are E and F mutually exclusive?

Two events A and B of a sample space S are mutually exclusive if the occurrence of any one of them excludes the occurence of the other event.Hence the two events A and B cannot occur simultaneously.
Thus $P(A\cap B)=0$
$\therefore$ Given a die is rolled.
Event E-die shows 4={4}
Event F-die shows even number {2,4,6}
$\therefore E \cap F$=${4}\neq\phi$
$\therefore E \cap F\neq\phi,E$ and $F$ are not mutually exclusive.