Question

A die is rolled. Let $E$ be the event “die shows $4$” and $F$ be the event “die shows even number”. Are $E$ and $F$ mutually exclusive?

Answer 1

When a die is rolled, the sample space is given by
$S = \\{1, 2, 3, 4, 5, 6\\}$
Accordingly, $E = {4}$ and $F = \\{2, 4, 6\\}$.

It is observed that $E ∩ F = {4} ≠Φ$
Therefore, $E$ and $F$ are not mutually exclusive events.