DfE statement P9 · Probability

Conditional probability

Higher onlyNon-calculator

Conditional probability is content statement P9 of the DfE GCSE mathematics subject content, in the probability area. It is Higher tier only, 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: "Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams." (statement P9). 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 P9

Tier

Higher tier only. A Foundation entry is never asked for this, so if you are sitting Foundation you can leave it out of your revision entirely.

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

Dividing by the overall total rather than by the total for the condition. P(A given B) has B's total on the bottom.
Swapping P(A given B) with P(B given A). They are different numbers and the question specifies which.
Reading the joint probability out of a Venn diagram and calling it the conditional one.

Formulae for this statement

The probability multiplication ruleP(A and B) = P(A) × P(B) for independent eventsBe able to derive this

Sample questions (10 of 30)

P9 · Conditional probabilityQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Probability

Advanced

In a survey, 120 adults were asked whether they have a driving licence. 70 of the adults are women and 50 are men. 45 of the women and 35 of the men have a driving licence. One of the adults who has a driving licence is picked at random. Work out the probability that this adult is a man.

💡 Hints:

Higher worksheet Higher probability practice

Nearby statements

P1Frequency of outcomes, tables and frequency trees P2Expected outcomes and fairness P3Relative frequency and the probability scale P4Probabilities of exhaustive events sum to one P5Empirical samples and sample size P6Sets, Venn diagrams and tree diagrams P7Possibility spaces for single and combined events

Questions people ask

Is conditional probability on Foundation or Higher?

Higher only. Foundation papers do not ask for it.

Can I use a calculator for conditional probability?

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?

Dividing by the overall total rather than by the total for the condition. P(A given B) has B's total on the bottom.

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.