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

Answer: C) rolling an even number and an odd number

Explanation:

For any event A and B , we say they are mutually exclusive if they are disjoint such that there have no elements in common.

Let's check all the options:

A) rolling a multiple of 2 and a multiple of 4

Multiple of 2 on dice = 2,4,6

Multiple of 4 on dice = 4

They are not disjoint since 4 is the common element.

B) rolling a multiple of 3 and a multiple of 6

Multiple of 3 on dice = 3,6

Multiple of 6 on dice = 6

They are not disjoint since 6 is the common element.

C) rolling an even number and an odd number

Even number on dice = 2,4,6

Odd number on dice = 1,3,5

∴ They are disjoint event as they have no common element.

D) rolling a prime number and an even number.

Prime number on dice = 2,3,5

They are not disjoint since 2 is the common element.

Answer 2

mutually exclusive is the events which couldn't happen at the same time, so I suggest you to go with this: C) rolling an even number and an odd number