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
$50$ 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
2
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
3
$80$ students were asked whether they play a musical instrument ( $M$ ) and whether they are in a sports team ( $S$ ). The Venn diagram shows the results.One of the $80$ students is chosen at random.

(a) Find $P(M \cup S)$ .

(b) Kai works out $P(M \cup S)$ by adding $P(M)$ and $P(S)$ together. Explain why Kai's method gives an answer that is too large.
Level 3 · 3 marksTry it
4
$40$ people were asked whether they drink tea ( $T$ ) and whether they drink coffee ( $C$ ).

The Venn diagram shows the results.One of the $40$ people is chosen at random.
(a) Work out the probability that this person drinks tea or coffee or both. (1 mark)
(b) Work out the probability that this person drinks neither. (1 mark)

One of the people who drinks tea is chosen at random.
(c) Work out the probability that this person also drinks coffee. (2 marks)
Level 3 · 4 marksTry it