Edexcel International GCSE Mathematics A · 4MA1
Venn diagram probability
A Venn diagram separates overlapping groups into non-overlapping regions. Fill the intersection first, then the exclusive parts of each set, and finally the outside region. Probabilities use the relevant population as the denominator, which changes under a condition.
Key method
n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The intersection is subtracted once because adding the set totals counts it twice.
Worked example
Of 30 students, 18 study French, 14 study Spanish and 8 study both. How many study neither?
- French only: 18 − 8 = 10. Spanish only: 14 − 8 = 6.
- At least one language: 10 + 8 + 6 = 24.
- Subtract from the whole group: 30 − 24 = 6.
Answer and interpretation
6 students; the probability for a randomly selected student is 6/30 = 1/5.
Common mistake
Subtracting 18 + 14 directly from 30 counts bilingual students twice.
Practise independently
Given that a student studies French, find the probability that they also study Spanish.
Check your answer
8/18 = 4/9; the condition restricts the denominator to the 18 French students.
Syllabus connection
This lesson develops venn diagram probability within the probability area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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