DfE statement P4 · Probability

Probabilities of exhaustive events sum to one

Both tiersNon-calculator

Probabilities of exhaustive events sum to one is content statement P4 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: "Apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one." (statement P4). 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 P4

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

Giving a set of probabilities that do not sum to 1, and not noticing.
Subtracting from 100 when working in fractions or decimals, so the answer comes out a hundred times too big.
Applying the rule to events that are not mutually exclusive, so the overlap is counted twice.

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)

P4 · Probabilities of exhaustive events sum to oneQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Probability

Beginner

A card is taken at random from an ordinary pack of 52 playing cards. The probability that the card is a diamond is 1/4. Work out the probability that the card is not a diamond.

💡 Hints:

Foundation worksheet Higher worksheet Foundation probability practice Higher probability practice

Nearby statements

P2Expected outcomes and fairness P3Relative frequency and the probability scale P5Empirical samples and sample size P6Sets, Venn diagrams and tree diagrams

Questions people ask

Is probabilities of exhaustive events sum to one on Foundation or Higher?

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

Can I use a calculator for probabilities of exhaustive events sum to one?

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?

Giving a set of probabilities that do not sum to 1, and not noticing.

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.