Knowledge Organiser: Venn Diagrams
Part of Venn Diagrams · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Venn Diagrams within Venn Diagrams for GCSE Mathematics. Revise Venn Diagrams in Probability for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 7 of 7 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 7 of 7
Practice
14 questions
Recall
12 flashcards
Knowledge Organiser: Venn Diagrams
Key Terms
- Universal set (U): Rectangle containing all possible outcomes
- Intersection (A ∩ B): The overlap — outcomes where BOTH events occur
- Union (A ∪ B): All outcomes where AT LEAST ONE event occurs
- Complement (A'): All outcomes NOT in set A
- Mutually exclusive: Events with no overlap — A ∩ B = 0
- Only A: In A but not in B (= n(A) − n(A ∩ B))
Must-Know Facts
- Always fill in the intersection (A ∩ B) first
- Only A = n(A) − n(A ∩ B); Only B = n(B) − n(A ∩ B)
- Neither = total − all other regions
- All four regions must sum to the grand total
- "At least one" means union (A ∪ B)
- P(A') = 1 − P(A)
- Use conditional probability: P(A|B) = P(A ∩ B) ÷ P(B)
Key Formulas
- P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
- P(A') = 1 − P(A)
- P(A|B) = P(A ∩ B) ÷ P(B)
- n(only A) = n(A) − n(A ∩ B)
Common Mistakes
- Double-counting the intersection: Numbers in the intersection belong to BOTH sets — don't count them again when filling the outer part of each circle
- Forgetting the outside region: Elements not in any set go outside all circles — total must equal the universal set
- P(A ∪ B) = P(A) + P(B): Wrong if sets overlap — must subtract P(A ∩ B) to avoid double-counting
- A' (complement): A' includes everything NOT in A, including the outside region and any other sets
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Read this section alongside the surrounding pages in Venn Diagrams. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Venn Diagrams
In a Venn diagram with two events A and B, which symbol represents the region where BOTH events occur at the same time?
A student claims: 'To find P(A ∪ B), you simply add P(A) and P(B).' Explain why this is not always correct, and state the correct formula with a reason.
Quick Recall Flashcards
14 questions on Venn Diagrams — practise free
Instant marking, adaptive difficulty, and 12 spaced repetition flashcards. Free until your GCSEs.
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