GCSE Maths: Probability

Probability at GCSE runs from single-event basics to the Higher tier conditional reasoning that feeds directly into A-Level statistics. This quiz covers the whole span in ten self-contained questions with concrete numbers throughout.

The foundations come first: probability as a value between 0 and 1, the complement rule through a "NOT red" question, and the addition rule for mutually exclusive events (P(A) = 0.35, P(B) = 0.45 giving P(A or B) = 0.80). Relative frequency appears through a biased coin tossed 200 times — the experimental probability question format that distinguishes observed frequency from theoretical probability — and expected outcomes through a defect-rate question scaling a proportion up to a sample.

Representation techniques get dedicated questions: sample space diagrams for two dice rolls, and a Venn-style two-set problem about students studying French and German, where the overlap must be subtracted to find "only French" — the single most common Venn diagram error. Independence is tested conceptually, asking which scenarios genuinely involve independent events.

The Higher tier material centres on probability without replacement: picking two white marbles from a bag of ten, where the second probability must change to 3/9 because the first marble is not returned — the tree-diagram skill that separates grade 6 from grade 4 answers. Every explanation shows the full calculation, and the distractors are the standard traps: adding when multiplication is needed, forgetting to update the denominator after the first pick, and treating overlapping sets as disjoint.

Paired with the Statistics quiz in this collection, the set completes the Probability and Statistics strand of the specification.

• Use the probability scale, complements and the addition rule for mutually exclusive events
• Distinguish relative frequency from theoretical probability and compute expected outcomes
• Enumerate outcomes with sample space diagrams and solve two-set Venn problems
• Identify independent events and multiply probabilities correctly
• Handle dependent events without replacement, updating probabilities at each stage (Higher)

Topic scope follows the Probability strand of the Department for Education's GCSE mathematics subject content: the 0–1 probability scale, mutually exclusive and exhaustive events, relative frequency, sample spaces, Venn and tree diagrams, and (Higher) conditional probability including without-replacement problems.