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 B are mutually exclusive and exhaustive

Options

• True

• False

Answer 1

This statement is True.

Reason:

A: The first die has an even number

B: The first die has an odd number

A ∪ B = The first die can have any number, even or odd, the second die can have any number from 1 to 6.

That is, A and B are mutually exclusive and exhaustive events.