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

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.