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ProbabilityDeep Dive

Systematic Listing Methods

Part of Sample Spaces · GCSE GCSE Mathematics revision

This deep dive covers Systematic Listing Methods within Sample Spaces for GCSE Mathematics. Revise Sample Spaces in Probability for GCSE Mathematics with 11 exam-style questions and 20 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 4 of 7 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 4 of 7

Practice

11 questions

Recall

20 flashcards

Systematic Listing Methods

Method 1: Tree Diagrams

Tree diagrams help visualize all possible outcomes systematically.

Example: Two Coin Flips
First Coin    Second Coin    Outcome
    H   ———————   H   ———————   HH
    |   ———————   T   ———————   HT
    |
    T   ———————   H   ———————   TH
        ———————   T   ———————   TT

Method 2: Tables/Grids

Useful when dealing with two separate experiments.

Example: Rolling Two Dice
Die 1 \ Die 2 1 2 3 4 5 6
1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
... ... ... ... ... ... ...

Total outcomes: 6 × 6 = 36

Method 3: Multiplication Principle

If one event has m outcomes and another has n outcomes, together they have m × n outcomes.

Examples:
  • Two coins: 2 × 2 = 4 outcomes
  • Three coins: 2 × 2 × 2 = 8 outcomes
  • Die and coin: 6 × 2 = 12 outcomes
  • Two dice: 6 × 6 = 36 outcomes

Keep building this topic

Read this section alongside the surrounding pages in Sample Spaces. That gives you the full topic sequence instead of a single isolated revision point.

Sample Space ExamplesExam TipsMapping All PossibilitiesKey Facts

Practice Questions for Sample Spaces

A fair coin is flipped and a fair die (numbered 1 to 6) is rolled. How many possible outcomes are there in total?

  • A. 6
  • B. 8
  • C. 12
  • D. 36
1 markfoundation

Explain what a sample space diagram is and why it is useful when finding probabilities for two combined events.

2 marksstandard

Quick Recall Flashcards

What is a sample space?
The set of all possible outcomes of an experiment
What is an outcome?
A single result from an experiment

11 questions on Sample Spaces — practise free

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