This deep dive covers Venn Diagram Applications 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 4 of 7 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 4 of 7
Practice
14 questions
Recall
12 flashcards
Venn Diagram Applications
Example 1: Survey Data
Problem: In a class of 30 students:
- 18 students play football (F)
- 12 students play tennis (T)
- 8 students play both sports
Step-by-Step Solution:
Step 1: Start with the intersection (both)
Students who play both: 8
Step 2: Find "only" regions
Only football: 18 - 8 = 10
Only tennis: 12 - 8 = 4
Step 3: Find "neither"
Neither sport: 30 - (10 + 8 + 4) = 8
Step 4: Check total
Total: 10 + 8 + 4 + 8 = 30 ✓
Probability Calculations
Using the same example:
- P(F) = 18/30 = 3/5
- P(T) = 12/30 = 2/5
- P(F ∩ T) = 8/30 = 4/15
- P(F ∪ T) = 22/30 = 11/15
- P(F') = 12/30 = 2/5
Key Formulas
Addition Rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Complement Rule: P(A') = 1 - P(A)
Conditional Probability: P(A|B) = P(A ∩ B) / P(B)
Example 2: Conditional Probability
Using the sports example:
Find: P(plays tennis | plays football)
P(T|F) = P(T ∩ F) / P(F) = (8/30) / (18/30) = 8/18 = 4/9
Meaning: Of the students who play football, 4/9 also play tennis
Keep building this topic
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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