Browse Venn diagrams & set notation

35 questions at your level

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

Venn diagrams

13 questions

LessonNot started

Owen carried out a survey of

90

people.

He asked each person if they like apples (

A

B

G

).

9

people like all three fruits.

23

people like apples and bananas.

11

people like apples and grapes but not bananas.

16

people like bananas and grapes.

44

people like grapes.

54

people like apples.

6

people like only bananas.
(a) Complete the Venn diagram for this information.(4 marks)

One of the

90

people is chosen at random.

Given that this person likes grapes,
(b) find the probability that this person also likes bananas.

(2 marks)

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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.

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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.

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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

N

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

pupils play none of the three sports.

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Set notation

11 questions

LessonNot started

30

students in a class.

W

is the set of students who walk to school and

L

is the set of students who have a school lunch.

The Venn diagram shows the numbers of students inside the circles. The number of students outside both circles has been left off.(a) Write down

n(W \cap L')

.

(b) Find

n\big((W \cup L)'\big)

.

(c) Explain why

n(W' \cap L')

must give the same answer as part (b), without doing a second calculation.

●●●●●Level 45 marksStart

\xi

is the set of the

50

members of a running club.

A

is the set of members who have run a marathon.

B

is the set of members who have run a half marathon.

n(A) = 26

n(B) = 21

n(A \cap B) = 8

.

(a) Find

n(A \cup B)

.

(b) Find

n(A \cap B')

.

(c) Find

n(A' \cap B')

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40

members of a sports club were asked which of football (

F

N

T

) they play.

The Venn diagram shows the results.(a) Write down

n(F \cap N)

.

(b) Find

n(F \cup T)

.

(c) Write down

n(F \cap N \cap T')

.

(d) Find

n(N')

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Probability from Venn diagrams

12 questions

LessonNot started

30

members of a music club were asked whether they play the guitar (

G

) and whether they play the violin (

V

). The Venn diagram shows the results.One member is chosen at random.

(a) Find the probability that this member plays the violin.

(b) Given that the chosen member plays the violin, find the probability that they also play the guitar.

●●●●●Level 44 marksStart

60

students were asked which of swimming (

S

T

) and running (

R

) they take part in. The Venn diagram shows the results.One of the

60

students is chosen at random.

(a) Find the probability that the student takes part in all three activities.

(b) Find the probability that the student swims.

(c) Find the probability that the student takes part in exactly one of the three activities.

●●●●●Level 45 marksStart