DfE statement P7 · Probability

Possibility spaces for single and combined events

Both tiersNon-calculator

Possibility spaces for single and combined events is content statement P7 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: "Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities." (statement P7). 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 P7

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

Listing (1, 2) and (2, 1) as one outcome when rolling two dice, which reduces 36 outcomes to 21 and makes every probability wrong.
Giving a sample space of 12 for two dice by adding 6 and 6 instead of multiplying.
Assuming outcomes are equally likely when the possibility space shows they are not — a total of 7 occurs six ways, a total of 2 only one.

Sample questions (10 of 30)

P7 · Possibility spaces for single and combined eventsQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Probability

Intermediate

Bag A contains 3 red balls and 2 blue balls. Bag B contains 1 red ball and 3 blue balls. One ball is taken at random from each bag. Work out the probability that both balls are red.

💡 Hints:

Foundation worksheet Higher worksheet Foundation probability practice Higher probability practice

Nearby statements

P5Empirical samples and sample size P6Sets, Venn diagrams and tree diagrams P8Independent and dependent combined events P9Conditional probabilityHigher only

Questions people ask

Is possibility spaces for single and 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 possibility spaces for single and 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?

Listing (1, 2) and (2, 1) as one outcome when rolling two dice, which reduces 36 outcomes to 21 and makes every probability wrong.

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.