1
1 The Venn diagram shows the number of students in a class of 40 who study physics (P), mathematics (M)
and geography (G).
(a) Use set notation to describe the shaded region.
................................................... [1]
(b) Find .
................................................... [1]
(c) A student is chosen at random from those studying geography.
Find the probability that this student also studies physics or mathematics but not both.
................................................... [2]
[Total: 4]
2
Use set notation to describe the shaded region.
................................................... [1]
[Total: 1]
C D
b m
h k
f j p
g y
Find n(C).
................................................... [1]
[Total: 1]
A B
Use set notation to describe the shaded region.
................................................... [1]
3
[Total: 1]
5 The Venn diagram shows the number of students in a group of 50 students who wear glasses (G), who wear
trainers (T) and who have a mobile phone (M).
G
T
0 2 3
2
19 14
1
M 9
(a) Use set notation to describe the region that contains only one student.
................................................... [1]
(b) Find .
................................................... [1]
(c) One student is picked at random from the 50 students.
Find the probability that this student wears trainers but does not wear glasses.
................................................... [1]
(d) Two students are picked at random from those wearing trainers.
Find the probability that both students have mobile phones.
................................................... [3]
[Total: 6]
4
6 There are 50 families in a village.
C = {families who own a car}
B = {families who own a bicycle}
23 families own a car.
10 families own a car and a bicycle.
6 families own no cars and no bicycles.
(a) Complete the Venn diagram.
[2]
(b) Find .
...................................................... [1]
[Total: 3]
A B
Use set notation to describe the shaded region.
........................................ [1]
[Total: 1]
8 A group of 120 students take two tests, mathematics and English.
Here is some information about the number of students who pass mathematics (M) and who pass English (E).
5
• 61 students pass mathematics.
• 27 students pass both mathematics and English.
• 19 students do not pass mathematics and do not pass English.
M E
(a) Complete the Venn diagram. [3]
(b) Use the Venn diagram to find n(E).
...................................... [1]
[Total: 4]
9
= {integers greater than 2}
A = {prime numbers}
B = {odd numbers}
C = {square numbers}
(a) Describe the type of numbers in the set .
.................................................................................. [1]
(b) Complete the set labels on the Venn diagram.
.......... ..........
..........
[1]
[Total: 2]
6
10 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
E = {x: x is an even number}
M = {x: x is a multiple of 3}
E M
(a) Complete the Venn diagram. [2]
(b) Write down .
................................................... [1]
(c) A number is chosen at random from the universal set .
Write down the probability that the number is in the set .
................................................... [2]
[Total: 5]
11 135 girls are asked if they like soccer (S) and if they like hockey (H).
n(S) = 53, n(H) = 68 and = 110.
7
(a) Complete the Venn diagram.
S H
...................... .......... ......................
......................
[3]
(b) Write down .
................................................... [1]
[Total: 4]
12 A baker asks some customers if they like lemon cake (L) and if they like chocolate cake (C).
The Venn diagram shows the results.
L C
Kab Bel
Yesa
Jai
Haji Var
Rea Nera
Esh Ada
Chir
Taj
(a) Work out the fraction of the customers who like lemon cake or chocolate cake but not both.
................................................... [1]
8
(b) Use set notation to complete the statement.
{Jai, Nera} = .............................. [1]
(c) What does the Venn diagram show about Taj?
.......................................................................................................................................................... [1]
[Total: 3]
13 In a class of 40 students:
• 28 wear glasses (G)
• 13 have driving lessons (D)
• 4 do not wear glasses and do not have driving lessons.
(a) Complete the Venn diagram. [2]
(b) Use set notation to describe the region that contains a total of 32 students.
................................................... [1]
[Total: 3]
9
14 Use set notation to describe the shaded region in each Venn diagram.
[2]
[Total: 2]
15 The Venn diagram shows information about the number of students in a class who like apples (A) and
bananas (B).
(a) Work out the number of students in the class.
................................................... [1]
10
(b) Work out the number of students who like bananas.
................................................... [1]
(c) Work out .
................................................... [1]
(d) How many more students like apples than like bananas?
................................................... [1]
(e) One of the students is chosen at random.
Find the probability that this student does not like apples and does not like bananas.
................................................... [1]
[Total: 5]
16 This Venn diagram shows information about the number of students who play basketball (B), football (F)
and hockey (H).
Find .
................................................... [1]
[Total: 1]
17 x is an integer.
= {x : }
11
A = {x : x is an odd number}
B = {x : x is a multiple of 3}
C = {x : x is a prime number}
(a) Complete the Venn diagram to show this information.
[3]
(b) List the elements of
(i) ,
................................................... [1]
(ii) .
................................................... [1]
(c) Find .
................................................... [1]
[Total: 6]
18 The Venn diagram below shows information about the number of gardeners who grow melons (M), potatoes
(P) and carrots (C).
12
(a) A gardener is chosen at random from the gardeners who grow melons.
Find the probability that this gardener does not grow carrots.
................................................... [2]
(b) Find .
................................................... [1]
[Total: 3]
19 50 students study at least one of the subjects geography (G), mathematics (M) and history (H).
18 study only mathematics.
19 study two or three of these subjects.
23 study geography.
The Venn diagram below is to be used to show this information.
13
(a) Show that x = 4.
[2]
(b) Complete the Venn diagram. [2]
(c) Use set notation to complete this statement.
.............................. [1]
(d) Find .
................................................... [1]
[Total: 6]
20 The Venn diagram shows two sets, A and B.
14
(a) Use set notation to complete the statements.
(i) d .............................. A [1]
(ii) {f, g} = .............................. [1]
(b) Complete the statement.
n ( .............................. ) = 6 [1]
[Total: 3]
21 One day, the number of members using the exercise machines (E), the swimming pool (S) and the tennis
courts (T) at a sports club is shown on the Venn diagram.
(a) Find the number of members using only the tennis courts.
................................................... [1]
(b) Find the number of members using the swimming pool.
................................................... [1]
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(c) A member using the swimming pool is chosen at random.
Find the probability that this member also uses the tennis courts and the exercise machines.
................................................... [2]
(d) Find .
................................................... [1]
[Total: 5]
22 (a) Use set notation to complete the statements for the Venn diagram above.
(i) c .............................. X [1]
(ii) .............................. = { a, m, e } [1]
(iii) .............................. [1]
(b) List the elements of .
................................................... [1]
(c) Find .
................................................... [1]
[Total: 5]
23
P Q
3 5 10
The Venn diagram shows the number of elements in each set.
(a) Find n(P '∩Q).
Answer(a) ................................................... [1]
16
(b) Complete the statement n( .........................................) = 17. [1]
[Total: 2]
