Knowledge Organiser: Sample Spaces
Part of Sample Spaces · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Sample Spaces 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 7 of 7 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 7 of 7
Practice
11 questions
Recall
20 flashcards
Knowledge Organiser: Sample Spaces
Key Terms
- Sample space (S): The set of ALL possible outcomes of an experiment
- Outcome: A single result from one trial of an experiment
- Event: A subset of the sample space (one or more outcomes)
- n(S): The number of outcomes in the sample space
- Equally likely outcomes: Each outcome has the same probability
- Multiplication principle: If event 1 has m outcomes and event 2 has n outcomes, together they have m × n outcomes
Must-Know Facts
- For equally likely outcomes: P(event) = n(event) ÷ n(S)
- Two coins give 4 outcomes: {HH, HT, TH, TT}
- Two dice give 36 outcomes (6 × 6)
- Three coins give 8 outcomes (2 × 2 × 2)
- Use a grid/table to list outcomes for two simultaneous events
- Order matters — (1, 2) and (2, 1) are different outcomes
- Always verify count using the multiplication principle
Key Methods
- Tree diagram — list all paths through multi-stage events
- Grid/table — list all combinations of two events
- Multiplication principle — m × n gives total outcomes for two events
- P(event) = number of favourable outcomes ÷ n(S)
Key Formulas
- Total outcomes for two events: n(A) × n(B) (multiplication principle)
- P(event) = favourable outcomes ÷ total outcomes in sample space
- Grid columns = outcomes of event 1; Grid rows = outcomes of event 2
Common Mistakes
- Missing outcomes: List all outcomes systematically — use a grid or tree diagram to avoid gaps
- Counting duplicates: (H, T) and (T, H) are different outcomes in a sample space — both must be counted
- Total outcomes wrong: For a fair die and coin: 6 × 2 = 12 total outcomes, not 6 + 2 = 8
- Reading probability from sample space: Count the favourable cells in the grid, then divide by total cells
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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?
Explain what a sample space diagram is and why it is useful when finding probabilities for two combined events.
Quick Recall Flashcards
11 questions on Sample Spaces — practise free
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