# Use Mutually Exclusive Events

In this worksheet, students explore mutually exclusive events.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Probability

Curriculum subtopic:   Probability, Basic Probability and Experiments

Difficulty level:

### QUESTION 1 of 10

Mutually exclusive events are events in probability are events that cannot happen at the same time.

Examples:

If I flip a coin, getting a head and getting a tail would be mutually exclusive because they cannot happen at the same time

If I rolled a dice, getting a 2 and getting an even number are not mutually exclusive because they can happen at the same time.

Mutually exclusive events are events that...

If I roll a dice, are getting an even and getting an odd number mutually exclusive?

Yes

No

If I roll a dice, are getting a prime number and getting an even number mutually exclusive?

Yes

No

Are these events mutually exclusive or not?

For each of these events, select if they are mutually exclusive, exhaustive or neither.

 Mutually Exclusive Exhaustive Neither getting a 1 and getting a 2 on a dice getting a heads and getting a tail on a coin Getting a heart and getting a picture cards from a deck of cards Getting a red card and getting a black card from a deck of cards

I pick a letter at random from the word MATHEMATICS.

Which of the following options are mutually exclusive?

S and T

S and a vowel

vowel and a consonant

S and a consonant

In the morning I drink either coffee, tea or orange juice.

Are there any options that are not mutually exclusive?

Yes

No

Throwing a head on a coin and throwing a tail are mutually exclusive because they can't happen at the ...

Yes

No

I pick one guest at a wedding at random. Which of the following are not mutually exclusive events?

Picking a make guest and picking a female guest

Picking a male guest and picking a guest over 65

Picking a femal e guest and picking a guest who is married

True or False

Mutually exclusive events are always exhaustive.

True

False

• Question 1

Mutually exclusive events are events that...

EDDIE SAYS
Exclusive means that only one of the two events can happen at the same time.
• Question 2

If I roll a dice, are getting an even and getting an odd number mutually exclusive?

Yes
EDDIE SAYS
If you roll a dice once, you cant get a number that is both even and odd so they are mutually exclusive.
• Question 3

If I roll a dice, are getting a prime number and getting an even number mutually exclusive?

No
EDDIE SAYS
If you roll a dice once, you can get a number that is both even and prime (the number 2) so these events are not mutually exclusive.
• Question 4

Are these events mutually exclusive or not?

EDDIE SAYS
Can you get a 6 and an even at the same time? Yes Can you get a spade (which is black) and a red card at the same time? No
• Question 5

For each of these events, select if they are mutually exclusive, exhaustive or neither.

 Mutually Exclusive Exhaustive Neither getting a 1 and getting a 2 on a dice getting a heads and getting a tail on a coin Getting a heart and getting a picture cards from a deck of cards Getting a red card and getting a black card from a deck of cards
EDDIE SAYS
Remember that exhaustive means it describes everything that could happen and Mutually Exclusive means they can't happen at the same time.
• Question 6

I pick a letter at random from the word MATHEMATICS.

Which of the following options are mutually exclusive?

S and T
S and a vowel
vowel and a consonant
EDDIE SAYS
Remember that things are Mutually Exclusive if they cannot happen together. The only one that can happen is getting an S and a consonant. (A vowel is A, E, I, O and U, a consonant is everything else)
• Question 7

In the morning I drink either coffee, tea or orange juice.

Are there any options that are not mutually exclusive?

No
EDDIE SAYS
Because none of these drinks contain each other and I only have one, all the probabilities are mutually exclusive.
• Question 8

Throwing a head on a coin and throwing a tail are mutually exclusive because they can't happen at the ...

EDDIE SAYS
This is the crux of mutually exclusive events. If they cant happen at the same time they are mutually exclusive,
• Question 9

I pick one guest at a wedding at random. Which of the following are not mutually exclusive events?

Picking a male guest and picking a guest over 65
Picking a femal e guest and picking a guest who is married
EDDIE SAYS
We're looking for the ones which could both happen at the same time. The only one that can't happen at the same time is Male/Female.
• Question 10

True or False

Mutually exclusive events are always exhaustive.

False
EDDIE SAYS
They are exhaustive sometimes but not always. For example. Getting a head and a tail on a coin are mutually exclusive and exhaustive Getting a 1 and getting a 2 on a dice are mutually exclusive but not exhaustive
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started