Revising combined events & sample space the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Combined events & sample space GCSE” on the site for the complete guide.
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Key facts to remember
1A sample space lists all possible outcomes of an experiment.
2For two dice or two spinners, use a grid (sample space diagram) to list all outcomes.
3P(event) = number of favourable outcomes ÷ total number of outcomes.
4Outcomes in a sample space are all equally likely (assuming fair dice, coins etc.).
5P(A and B) = P(A) × P(B) only if A and B are independent events.
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Worked examples
Example 1
Two fair dice are rolled. Find the probability that the sum equals 7.
Working
Sample space: 6 × 6 = 36 equally likely outcomes
Outcomes summing to 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 outcomes
P(sum = 7) = 6/36 = 1/6
Answer1/6
Example 2
A coin is flipped and a fair 4-sided die is rolled. List the sample space and find P(H and even number).