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' , B' ,C are mutually exclusive and exhaustive.

Options

• True

• False

Answer 1

This statement is False.

Since A' = B and B' = A,

A' ∩ B' = Φ

B ∩ C = {(1, 1), (1, 2), (1, 3), (1, 4), (3, 1), (3, 2)} ≠ Φ

A ∩ C = {(2, 1), (2, 2), (2, 3), (4, 1)} ≠ Φ

Thus, A', B' and C are not mutually exclusive.