A Level Maths · Statistics · Year 12 and 13
Probability questions reward a good diagram. Venn diagrams, tree diagrams and two-way tables turn wordy questions into arithmetic; Year 13 adds conditional probability and set notation.
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AS content is usually taught in Year 12. The full A Level adds the Year 13 content. Sitting AS exams or mocks? See the AS Level Maths checklist.
Given that $P(X) = 0.4$, $P(Y) = 0.5$, and $P(X \cap Y) = 0.2$, find the conditional probability $P(X | Y)$.
Then practise: skills to practise · open probability practice questions.
Every board examines the same A Level Maths content, set by the Department for Education. Only the paper it appears on and the section numbering differ.
| Board | Specification reference | Examined in |
|---|---|---|
| AQA 7357 | AQA section M | Paper 3 |
| Edexcel 9MA0 | Edexcel topic Statistics 3 | Paper 3, Section A |
| OCR A H240 | OCR reference 2.03 | Paper 2, statistics section |
Statistics questions can be set in the context of your board's large data set: large data set guides and practice (Edexcel · AQA · OCR A).
Three examples from the question bank, one with its full mark scheme open. Every question comes with a step-by-step mark scheme (M, A and B marks) once you start practising.
Events $A$ and $B$ are mutually exclusive. Given that $P(A) = 0.3$ and $P(B) = 0.45$, find $P(A \cup B)$.
Mark scheme: in the 7-day free trial.
Given that $P(A) = 0.5$, $P(B) = 0.6$, and $P(A \cup B) = 0.85$, find $P(A \cap B)$.
Every question here has a full worked solution. See them all →
The probability that it rains on a given day is $0.4$. If it rains, the probability that Alice takes the bus is $0.8$. If it does not rain, the probability that she takes the bus is $0.3$. Given that Alice takes the bus, find the probability that it rained that day.
Mark scheme: in the 7-day free trial.
Questions are original and written in the style of Edexcel 9MA0, and cover content that AQA and OCR examine too. They are not past-paper questions.
Full question sets with mark schemes: conditional probability questions (15)
Revision notes: Probability: Venn diagrams, trees and independence · Conditional probability and modelling
These skills sit in the Statistics unit of the UK A Level practice engine. Pick any mix of them, set the difficulty, and check each answer against its mark scheme.
Probability can come up on these papers (from each board's paper structure). We haven't mapped individual questions yet, so open a recent paper and look for it.
| Board | Recent papers that can test it |
|---|---|
| Edexcel 9MA0 | Paper 3: June 2025, June 2024, June 2023 |
| AQA 7357 | Paper 3: June 2025, June 2024, June 2023 |
| OCR H240 | Paper 2: June 2025, June 2024, June 2023 |
Papers are © the exam boards; each page links to the official question paper and mark scheme. All A Level Maths past papers →
Yes. Probability is part of the A Level Maths content that every board examines: AQA section M, Edexcel Statistics 3, OCR 2.03. It is assessed in AQA Paper 3; Edexcel Paper 3, Section A; OCR A Paper 2, statistics section.
Both. The AS content, usually taught in Year 12, is: Mutually exclusive and independent events; Venn diagrams, tree diagrams and two-way tables. The full A Level adds: Conditional probability, including set notation P(A | B); Modelling with probability and questioning the assumptions.
Show that P(A ∩ B) = P(A) × P(B), or that P(A | B) = P(A). Say which one you are testing and write a conclusion.
Stretch yourself: original probability problems at Senior level (ages 16 to 18), with hints and full solutions: Problem S101 · Problem S29 · Problem S102 · Problem S30. All 20 →
Applying for maths, computer science or economics? TMUA practice on this topic: Statistics and probability. TMUA preparation: notes, questions and mock papers → Taking STEP? STEP-style problems: Probability and statistics.
Thinking about an EPQ? Maths EPQ ideas that use this topic: Modelling a school canteen queue · The 37% rule for choosing the best · Shared birthdays in real classes · all 93 ideas
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