DfE statement P8 · Probability

Independent and dependent combined events

Both tiersNon-calculator

Independent and dependent combined events is content statement P8 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: "Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions." (statement P8). 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 P8

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

Keeping the denominator unchanged on the second branch of a without-replacement tree. Both the numerator and the denominator drop.
Adding along the branches instead of multiplying, or multiplying between them instead of adding.
Assuming independence when the context makes the events dependent, and not stating the assumption when the question asks for it.

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)

P8 · Independent and dependent combined eventsQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Probability

Beginner

The probability that Ben catches his bus on time is 0.8. The probability that Freya catches her bus on time is 0.5. The two events are independent. Work out the probability that both Ben and Freya catch their bus on time.

💡 Hints:

Foundation worksheet Higher worksheet Foundation probability practice Higher probability practice

Nearby statements

P6Sets, Venn diagrams and tree diagrams P7Possibility spaces for single and combined events P9Conditional probabilityHigher only

Questions people ask

Is independent and dependent combined events on Foundation or Higher?

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

Can I use a calculator for independent and dependent combined events?

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?

Keeping the denominator unchanged on the second branch of a without-replacement tree. Both the numerator and the denominator drop.

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.