GCSE · Venn diagrams & set notation

Probability from Venn diagramsExam-style questions

Why the denominator is always the total in the universal set — outsiders included — where P(A ∪ B) = P(A) + P(B) − P(A ∩ B) comes from in the picture, and how a "given that" condition shrinks the denominator to one circle.

Start practising Read the lesson

11 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
Here is a Venn diagram for $40$ students showing who studies French (F) and Spanish (S).A student is picked at random. Work out the probability that they study both languages.
Level 1 · 1 markTry it
2
Here is a Venn diagram for $40$ students showing who studies French (F) and Spanish (S).A student is picked at random. Work out the probability that they study French.
Level 1 · 2 marksTry it
3
$40$ adults were asked whether they own a cat ( $C$ ) and whether they own a dog ( $D$ ). The Venn diagram shows the results.One of the $40$ adults is chosen at random.

(a) Find the probability that this adult owns a cat.

(b) Find the probability that this adult owns neither a cat nor a dog.
Level 2 · 3 marksTry it
4
$50$ people were asked whether they read a newspaper ( $N$ ) and whether they listen to the radio ( $R$ ). The Venn diagram shows the results.One of the $50$ people is chosen at random.

(a) Find $P(N \cup R)$ .

(b) Find $P(N')$ .
Level 3 · 4 marksTry it
5
The Venn diagram shows the probabilities for two events $A$ and $B$ .(a) Find $P(A)$ .

(b) Find $P(A \cup B)$ .

(c) Find $P(B')$ .
Level 3 · 6 marksTry it

6 more questions on probability from venn diagrams

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free