GCSE · Venn diagrams & set notation

Venn diagramsExam-style questions

Building a Venn diagram from worded information — why you fill the overlap first and work outwards, what the number in a region actually counts, the universal set and the "neither" region outside the circles, and how the grand total pins down whichever region is missing.

Start practising Read the lesson

13 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
$40$ people were asked whether they like tea and whether they like coffee.

$24$ of them like tea and $21$ of them like coffee.

The Venn diagram shows some of this information. $T$ is the group who like tea, $C$ is the group who like coffee, and $x$ is the number of people who like both.(a) Work out the value of $x$ .

(b) Write down how many of the $40$ people like tea but not coffee.
Level 4 · 4 marksTry it
2
$50$ students were asked which of the art club ( $A$ ), the drama club ( $D$ ) and the music club ( $M$ ) they attend.

The Venn diagram shows the results.(a) Work out how many students attend the art club.

(b) Work out how many students attend exactly two of the three clubs.

(c) Work out how many students attend at least one club.
Level 4 · 6 marksTry it
3
$60$ $60$ pupils were asked which of football, netball and rounders they play.
- $28$ play football,
- $25$ play netball,
- $22$ play rounders,
- $10$ play football and netball,
- $8$ play football and rounders,
- $9$ play netball and rounders,
- $4$ play all three sports.
Here is an empty Venn diagram, with the circles labelled $F$ $F$ (football), $N$ $N$ (netball) and $R$ $R$ (rounders).(a) Copy the diagram and write the correct number of pupils in each of the seven regions inside the circles.

(b) Work out how many of the $60$ $60$ pupils play none of the three sports.
Level 4 · 6 marksTry it
4
A school surveyed $140$ students about the devices they own: a laptop ( $L$ ), a tablet ( $T$ ) and a games console ( $G$ ).

$16$ students own none of these devices.

$53$ students own a laptop.

$38$ students own a games console.

$19$ students own a laptop and a tablet.

$15$ students own a laptop and a games console.

$11$ students own a tablet and a games console.

$7$ students own all three devices.
(a) Complete the Venn diagram for this information.(4 marks)

One of the students who own a games console is chosen at random.
(b) Work out the probability that this student does not own a laptop.

(2 marks)
Level 4 · 6 marksTry it