Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Use Sample Space Diagrams to Calculate Probability

In this worksheet, students will calculate probabilities using sample space diagrams.

'Use Sample Space Diagrams to Calculate Probability' worksheet

Key stage:  KS 3

Year:  Year 9 Maths worksheets

Curriculum topic:   Probability

Curriculum subtopic:   Enumerate Sets Using Tables, Grids and Diagrams

Difficulty level:  

Worksheet Overview

The following spinners are spun and the sum of the scores they landed on is recorded.


Do we know how to calculate how many possible outcomes are there?


spinner with four sections     spinner with four sections


Well, each spinner has 4 possible outcomes.

So altogether, there are 4 x 4 = 16 possible outcomes for the combined events (i.e. multiple events occurring at the same time).


The two scores are added together and so we can create a sample space diagram to show the possible totals:


  1 2 3 4
1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8


We can see that the possible sums are 2, 3, 4, 5, 6, 7 and 8.


These all have different frequencies though (the number of times they occur) so there still are 16 possible outcomes altogether!

The sum of 7 occurs 2 times out of 16 possible outcomes.

So the probability of getting a sum of 7 is P(7) = 2/16 = 1/8!


We call the set of all possible outcomes the sample space.

We can write it as a list or in a table - just like we did above!


Let's put this all into practice now!

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

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