Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Use Sample Space Diagrams

In this worksheet, students will practise listing all the outcomes of events by using a sample space diagram.

'Use Sample Space Diagrams' worksheet

Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Probability

Curriculum subtopic:   Probability Combined Events and Probability Diagrams

Popular topics:   Prime Numbers worksheets

Difficulty level:  

Worksheet Overview

What is a sample space diagram?

They are used to show all the outcomes of two events where the events are equally likely.

For example, you could use a sample space diagram when you roll dice, flip coins etc.


What does it look like?

All sample space diagrams have the same form - the outcomes for each event go along the top and the side, and the outcomes for the combined events go in the middle.


A sample space diagram


How do we fill one of these in?

This is easiest if we use an example:

I roll a dice and add the numbers together.

Draw a sample space diagram to show all the outcomes.


Step 1: Set up the outcomes for the individual events.

We know that on each dice we have the numbers 1 to 6.


A sample space diagram


Step 2: Fill in the middle.

I'll start with a random one - we are told that we add the numbers. If we roll two fours and add,

we will get 8.


A sample space diagram


We can now fill in the rest.


A sample space diagram


Will they always have numbers in the middle?

It depends on the question. For example, the outcomes of rolling a dice and flipping a coin can't be added together, so we just write both the outcomes.


A sample space diagram



Using a sample space diagram to find probabilities.



I roll two dice and add them together.

What is the chance that my numbers add to make a prime number?


We already know that the sample space diagram looks like the one above. If we want to find the probability that my result is a prime, we count all the ones that are prime.


A sample space diagram


From this, we can count that we have 15 prime numbers.

We have 36 numbers in the middle section (we don't count the outside numbers).

This gives a probability of 15/36 which can cancel to 5/12


Now let's have a go at some questions.

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

Popular Maths topics

Try an activity or get started for free

  • National Tutoring Awards 2023 Shortlisted / Parents
    National Tutoring Awards 2023 Shortlisted
  • Private-Tutoring-WINNER-EducationInvestor-Awards / Parents
    Winner - Private Tutoring
  • Bett Awards Finalist / Parents
  • Winner - Best for Home Learning / Parents
    Winner - Best for Home Learning / Parents