Question

$A$ die is rolled. Let $E$ be the event "die shows $4$" and $F$ be the event "die shows even number". Then, $E$ and $F$ are

• A. mutually exclusive
• B. exhaustive
• C. mutually exclusive and exhaustive
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Let $E =$ The event $''$die shows $4'' = \\{4\\}$ Let $F =$ The event "die shows an even number" $= \\{2, 4, 6\\}$ \therefore E \cap F = \left\\{4\right\\} \ne \phi Hence, $E$ and $F$ are not mutually exclusive.