DfE statement P6 · Probability

Sets, Venn diagrams and tree diagrams

Both tiersNon-calculator

Sets, Venn diagrams and tree diagrams is content statement P6 of the DfE GCSE mathematics subject content, in the probability area. It is on both tiers, and it is examined without a calculator. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams." (statement P6). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement P6

Tier

Both tiers. This statement is Foundation content, which means Higher students are examined on it too — Higher is Foundation plus more, never instead of it.

Calculator

This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.

Common mistakes

Counting the members of the intersection twice, once in each set, so the totals no longer match the given figures.
Forgetting the region outside both sets, which usually holds the members the question is really about.
Filling a Venn diagram from the outside in. Start with the intersection and subtract outwards.

Formulae for this statement

The probability addition ruleP(A or B) = P(A) + P(B) for mutually exclusive eventsBe able to derive this

Sample questions (10 of 30)

P6 · Sets, Venn diagrams and tree diagramsQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Probability

Beginner

A survey asks 40 people whether they own a cat, a dog, both, or neither. 12 people own only a cat, 15 own only a dog, 5 own both, and 8 own neither. Work out the probability that a randomly chosen person owns a cat or a dog (or both). Give your answer as a fraction in its simplest form.

💡 Hints:

Foundation worksheet Higher worksheet Foundation probability practice Higher probability practice

Nearby statements

P4Probabilities of exhaustive events sum to one P5Empirical samples and sample size P7Possibility spaces for single and combined events P8Independent and dependent combined events

Questions people ask

Is sets, Venn diagrams and tree diagrams on Foundation or Higher?

Both. It is Foundation content, so it can be asked on either tier.

Can I use a calculator for sets, Venn diagrams and tree diagrams?

Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.

What is the single most common mistake here?

Counting the members of the intersection twice, once in each set, so the totals no longer match the given figures.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

Back to Probability at Foundation or at Higher.