Topic explanation
Probability at GCSE starts with the idea that probabilities fall between 0 and 1 (or 0% and 100%), with mutually exclusive and independent events handled carefully. Exam questions often combine fractions, tree diagrams, and short written justification.
Boards reward showing logical steps: listing outcomes, using P(A) + P(not A) = 1, and matching the event described in the question (especially "at least one", "exactly one", "given").
Key formulas & rules
- P(A) = (number of favourable outcomes) / (total equally likely outcomes)
- For mutually exclusive events: P(A or B) = P(A) + P(B)
- For independent events: P(A and B) = P(A) × P(B)
- Complement: P(not A) = 1 − P(A)
Common mistakes
- Adding probabilities that are not mutually exclusive without adjusting for overlap.
- Treating "without replacement" as independent — use conditional probabilities / reduced counts.
- Using different denominators when combining branches on a tree without rescaling.
Exam tips
- Draw a small tree or sample space for joint events — it reduces slips under time pressure.
- Round only at the end if the question specifies decimal places; prefer exact fractions until then.
- Read "and" vs "or" carefully; "at least one" often pairs well with the complement rule.
Practice questions
Exam-style questions aligned to your board. Open full practice for worked feedback and your next best question.
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