GCSE Maths → Probability → Venn Diagrams
Venn Diagrams GCSE Maths
Venn diagrams are used in GCSE maths to show sets, groups, and overlaps. They are especially useful in probability questions where students need to organise information clearly.
Venn diagrams connect closely with probability basics and fractions.
Video explanation
A short Worthing Maths Tutor video explanation for Venn diagrams GCSE probability can be embedded here later to improve student engagement and time on page.
What is a Venn diagram?
A Venn diagram uses circles inside a rectangle. Each circle represents a set or group. The overlap shows items that are in both groups.
A ∪ B means A or B or both
Intersection: A and B
The intersection is the overlap between two sets. It means items that are in both groups.
Example 1: Intersection
In a class, 12 students play football, 10 play basketball, and 4 play both.
The number in the overlap is:
So 4 students are in the intersection.
Union: A or B
The union includes everything in either set, including the overlap.
Example 2: Union
12 students play football, 10 play basketball, and 4 play both. How many play football or basketball?
We subtract the overlap once because it was counted twice.
Completing a Venn diagram
Example 3: Fill in the regions
In a group of 30 students, 16 study French, 14 study German, and 5 study both.
Put the overlap in first:
French only:
German only:
Students studying at least one language:
Neither:
Using Venn diagrams for probability
Once the Venn diagram is complete, probability is found by dividing the required region by the total number of outcomes.
Example 4: Probability from a Venn diagram
In a group of 30 students, 11 study French only, 5 study both, 9 study German only, and 5 study neither.
Find the probability that a student studies French.
French includes French only and both:
Total students:
Probability:
Example 5: Probability of neither
If 5 out of 30 students study neither French nor German, then:
Common mistakes in Venn diagram questions
- Forgetting to put the overlap in first.
- Counting the overlap twice.
- Confusing “and” with “or”.
- Forgetting to include the overlap when finding a full set.
- Forgetting to simplify probability fractions.
Practice questions
- In a group of 40 students, 18 play football, 15 play tennis, and 6 play both. How many play football only?
- Using the same information, how many play tennis only?
- How many play football or tennis?
- How many play neither sport?
- What is the probability that a randomly chosen student plays both?
Answers
- 12
- 9
- 27
- 13
- 6/40 = 3/20
Venn diagrams FAQ
What is a Venn diagram?
A Venn diagram is a diagram that uses circles to show sets and how groups overlap.
What does intersection mean in a Venn diagram?
The intersection is the overlap between sets. It means items that are in both groups.
What does union mean in a Venn diagram?
The union means everything in either set, including the overlap.
Are Venn diagrams on GCSE maths?
Yes. Venn diagrams appear in GCSE maths, especially in probability and set notation questions.
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