Probability — A-Level Mathematics Revision
Revise Probability for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP.
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Go to Statistical DistributionsWhat 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 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.
Mini lesson for Probability
1. Understand the core idea
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.
Can you explain Probability without copying the notes?
2. Turn it into marks
A bag contains 5 red balls and 3 blue balls. Two balls are drawn without replacement.
Underline the method, evidence, or command-word move that would earn credit in A-Level Statistics.
3. Fix the likely mark leak
Watch for this mistake: Confusing 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.
Write one correction rule before doing another practice question.
Practise this topic
Jump into adaptive, exam-style questions for Probability. Free to start; sign in to save progress.
Probability practice questions
These are original StudyVector questions for revision practice. They are not official exam-board questions.
Question 1
In one A-Level sentence, explain what Probability is testing.
Answer: 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.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Probability question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Confusing 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." What should their next repair task be?
Answer: Do one Probability question and review the mistake type.
Mark focus: Error correction and next-step practice.
Probability flashcards
Core idea
What is the main idea in 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 concept...
Common mistake
What mistake should you avoid in Probability?
Confusing 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 b...
Practice
What is one useful practice task for Probability?
Answer one Probability question and review the mistake type.
Exam board
How should you use board notes for Probability?
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.
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
Exam-style questions for Probability with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Probability
Core concept
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 under…
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.