Question

Two dice are thrown. The events A, B and C are as follows:

A: getting an even number on the first die.

B: getting an odd number on the first die.

C: getting the sum of the numbers on the dice ≤ 5

State true or false: (give reason for your answer)

 A and C are mutually exclusive

Options

• True

• False

Answer 1

This statement is False.

Reason:

A = even number on the first dice

C = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1}}

A and C have (2, 1), (2, 2), (2, 3), (4, 1) as equal events.

∴ A ∩ C ≠ ϕ

Hence, A and C are not mutually exclusive.