Sample Space Diagrams

This lesson focuses on constructing and using sample space diagrams to list all outcomes for combined events. Sample space diagrams are a key tool in the Edexcel GCSE Mathematics (1MA1) probability topic and are regularly tested across Foundation and Higher papers.

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What Is a Sample Space Diagram?

A sample space diagram is a systematic way of listing all possible outcomes when two events are combined. It is usually drawn as a grid (table) with one event along the top and the other down the side.

The total number of outcomes = (number of outcomes for event 1) × (number of outcomes for event 2).

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Two Dice — Adding Scores

Worked Example 1

Two fair six-sided dice are rolled. Their scores are added together. Draw a sample space diagram and use it to find:

(a) P(total = 9) (b) P(total is at least 10) (c) P(total is a prime number)

Sample Space Diagram: