A-Level Mathematics Revision — Probability
Revise Probability for A-Level Mathematics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
At a glance
- What StudyVector is
- An exam-practice platform with board-aligned questions, explanations, and adaptive next steps.
- This topic
- Probability in A-Level Mathematics: explanation, examples, and practice links on this page.
- Who it’s for
- Students revising A-Level Mathematics for UK exams.
- Exam boards
- Check your course page and the topic board notes for supported specifications.
- Free plan
- Sign up free to use tutor paths and feedback on your answers. Free access is Free daily revision · No card required. Pricing
- What makes it different
- Syllabus-shaped practice and progress tracking—not generic AI answers.
This page includes a topic explanation and a worked example. Check your course for current practice coverage.
Next in this topic area
Next step: Statistical Distributions
Continue in the same course — structured practice and explanations on StudyVector.
Go to Statistical DistributionsTopic explanation
What is Probability?
Probability at A-Level builds on GCSE concepts by introducing conditional probability, Venn diagrams, and tree diagrams for more complex scenarios. You will learn to use probability formulae and understand the concepts of independence and mutual exclusivity.
Board notes: All A-Level Maths boards (AQA, Edexcel, OCR) cover probability in a similar way. The complexity of the problems and the use of Venn diagrams and tree diagrams are consistent across all boards.
Step-by-step explanationWorked examples
Worked example
A bag contains 5 red balls and 3 blue balls. Two balls are drawn without replacement. What is the probability that both balls are red? The probability of the first ball being red is 5/8. The probability of the second ball being red, given the first was red, is 4/7. So, the probability of both being red is (5/8) * (4/7) = 20/56 = 5/14.
Practise this topic
Start with low-focus cards for Probability, then move into full exam-style practice when you want the heavier session.
Common mistakes
- 1Confusing the concepts of independence and mutual exclusivity. Two events are independent if the occurrence of one does not affect the probability of the other, while two events are mutually exclusive if they cannot both happen at the same time.
- 2Incorrectly using the formula for conditional probability, P(A|B) = P(A and B) / P(B).
- 3Making errors in setting up or interpreting Venn diagrams, particularly with the placement of probabilities in the correct regions.
Probability exam questions
Check the available question sets for Probability. Use your course and exam board to confirm which practice is relevant.
Probability exam questionsGet help with Probability
Get a personalised explanation for Probability from the StudyVector tutor. Ask follow-up questions and work through problems with step-by-step support.
Open tutorSave your progress in Probability
Start a free account for low-focus question cards, feedback and Play routes across available topics. Free daily limits apply; no card required.
Continue your revision
A public question for Probability is still being reviewed. Your course page shows the topics currently available for practice.
Continue with Probability
Create a free account to keep your course choice and save your practice progress.
Start free low-focus cardsAlready have an account? Log in
Frequently asked questions
What is the difference between P(A and B) and P(A or B)?
P(A and B) is the probability that both event A and event B occur. P(A or B) is the probability that either event A or event B or both occur. The formula is P(A or B) = P(A) + P(B) - P(A and B).
How do I know if two events are independent?
Two events A and B are independent if P(A and B) = P(A) * P(B). If this condition is not met, the events are not independent.