Question

You roll a six-sided number cube. Which events are mutually exclusive?

A) rolling a multiple of 2 and a multiple of 4
B) rolling a multiple of 3 and a multiple of 6
C) rolling an even number and an odd number
D) rolling a prime number and an even number

Answer 1

Events are mutually exclusive only if they cannot both be true.
Only C is alright.

4 is a multiple of two so it can't be right.
Same logic works for B.

And then 2 is prime so then D is out too.

Answer 2

C) Rolling an even number and an odd number.

Explanation:

We are asked to choose the correct option that represents two mutually exclusive events.

Since we know that mutually exclusive events are those events, who can not happen at the same time. As we cannot have both heads and tails in one toss, either we will get heads or we will get tails.

Let us check our given choices one by one.

A) Rolling a multiple of 2 and a multiple of 4.

Multiples of 2: 2, 4, 6,..

Since 4 is a multiple of 2, so both events are not mutually exclusive and option A is not a correct choice.

B) Rolling a multiple of 3 and a multiple of 6.

Multiples of 3: 3, 6, 9,...

Since 6 is a multiple of 3, so both events are not mutually exclusive and option B is not a correct choice.

C) Rolling an even number and an odd number.

Odd numbers on a cube: 1, 3, 5.

Even numbers on a cube: 2, 4, 6.

Since on one roll of dice we can either have an odd or an even number, both events are not possible with a single roll, therefore, option C is the correct choice.

D) Rolling a prime number and an even number.

Prime number on a cube: 2, 3, 5.

Even numbers on a cube: 2, 4, 6.

We can clearly see that 2 is a prime number and it is even as well, therefore, option D is not a correct choice.