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GCSE Foundation · grades 1–5 · 7.5% of marks

GCSE Foundation — Probability

Every probability statement a GCSE Foundation student may be asked is here; together they are 7.5% of the assessment. 8 statements make up probability here. Each has its own page with the specification wording, the common mistakes, and questions. The ground it covers runs through frequency of outcomes, tables and frequency trees, expected outcomes and fairness, relative frequency and the probability scale, probabilities of exhaustive events sum to one, empirical samples and sample size and sets, Venn diagrams and tree diagrams. Everything on this page is Foundation content, which means a Higher student needs it too — Higher is Foundation plus more, not instead of. With 50% AO1 and 50% across AO2 and AO3, fluency alone is not enough — the paper repeatedly asks what your answer means. The bulk of it sits comfortably on the non-calculator paper; a calculator quietly hides the gap until the exam.

  • P1 — Frequency of outcomes, tables and frequency trees
  • P2 — Expected outcomes and fairness
  • P3 — Relative frequency and the probability scale
  • P4 — Probabilities of exhaustive events sum to one
  • P5 — Empirical samples and sample size
  • P6 — Sets, Venn diagrams and tree diagrams
  • P7 — Possibility spaces for single and combined events
  • P8 — Independent and dependent combined events

Practise

GCSE Foundation · ProbabilityQuestion 1 of 20 · 0 correct
Practice mode· no pressure · hints available

Probability

P6

Intermediate

A Venn diagram shows two sets, P and Q, inside a universal set. n(P) = 34, n(Q) = 27, n(P ∩ Q) = 11, and n(ξ) = 90, where ξ is the universal set. Work out n((P ∪ Q)′), the number of elements in neither P nor Q.

💡 Hints:
Printable worksheetNon-calculator sheetSample Paper 1Sample Paper 2

The 8 DfE statements in probability at Foundation

Higher-only statements are not listed here; statements with a Higher-only part are marked and the part is quoted.

P1Frequency of outcomes, tables and frequency treeseither paper
30 questions
P2Expected outcomes and fairnesseither paper
30 questions
P3Relative frequency and the probability scaleeither paper
30 questions
P4Probabilities of exhaustive events sum to onenon-calculator
30 questions
P5Empirical samples and sample sizeeither paper
14 questions
P6Sets, Venn diagrams and tree diagramsnon-calculator
30 questions
P7Possibility spaces for single and combined eventsnon-calculator
30 questions
P8Independent and dependent combined eventsnon-calculator
30 questions

Related

Probability at Higher7.5% of Higher marksStatisticsFoundation · 7.5% of marksRatio, proportion and rates of changeFoundation · 25% of marksNumberFoundation · 25% of marks

Questions people ask

How much of the GCSE Foundation paper is probability?

7.5% of the total marks, and the three papers each carry an equal share of the qualification, so it is spread across all of them rather than concentrated in one.

How many topics are there in probability at GCSE Foundation?

8 DfE content statements, coded P1 to P8 within this area. Every question in the bank is tagged to one of them.

Is any probability content on this page Higher only?

No. Foundation pages only show statements a Foundation entry may be asked. The Higher-only probability material is on the GCSE Higher page for this area.

Can I use a calculator for probability questions?

Paper 1 is non-calculator; Papers 2 and 3 allow one. Of the 8 statements in this area, 4 are naturally non-calculator and 0 naturally calculator, with the rest workable either way — so practise both.

What kind of marks does probability carry?

The GCSE Foundation split is 50% AO1 (use and apply standard techniques), 25% AO2 (reason, interpret and communicate) and 25% AO3 (solve problems in and out of context). Questions in this area are set across all three.

Are these past paper questions?

No. Every question at /gcse-foundation is original, written to the DfE content statements and checked before it is published. We do not host past papers or mark schemes.

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