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Venn diagrams & set notation
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35 questions at your level
Difficulty
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Level 1
Level 2
Level 3
Level 4
Level 5
Venn diagrams
13 questions
Lesson
Not started
Mark as done
50
50
50
people were asked whether they had visited France (
F
F
F
) or Spain (
S
S
S
).
28
28
28
had visited France,
24
24
24
had visited Spain, and
6
6
6
had visited neither.
(a)
Work out how many people had visited both France and Spain. (2 marks)
(b)
One of the
50
50
50
people is chosen at random. Work out the probability that they had visited France but not Spain. (1 mark)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
85
85
85
students were asked whether they study Spanish and whether they study German.
47
47
47
study Spanish,
33
33
33
study German,
15
15
15
study both Spanish and German.
(a)
Draw a Venn diagram to show this information.
(b)
Work out how many of the
85
85
85
students study exactly one of the two languages.
●●●
●●
Level 3
5 marks
Start
→
Mark as done
A sports club has
50
50
50
members.
26
26
26
of the members play badminton,
19
19
19
play squash and
8
8
8
play both badminton and squash.
(a)
Work out how many members play neither badminton nor squash.
(b)
Sam says: "
26
+
19
=
45
26 + 19 = 45
26
+
19
=
45
, and
50
−
45
=
5
50 - 45 = 5
50
−
45
=
5
, so
5
5
5
members play neither."
Explain why Sam's method is wrong.
●●●
●●
Level 3
4 marks
Start
→
Set notation
11 questions
Lesson
Not started
Mark as done
30
30
30
students were asked whether they play hockey (
H
H
H
) and whether they play netball (
N
N
N
).
The Venn diagram shows the results.
ξ
3
H
N
12
7
8
(a)
Write down
n
(
H
∩
N
)
n(H \cap N)
n
(
H
∩
N
)
.
(b)
Find
n
(
H
∪
N
)
n(H \cup N)
n
(
H
∪
N
)
.
(c)
Write down
n
(
H
∩
N
′
)
n(H \cap N')
n
(
H
∩
N
′
)
.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
ξ
=
{
1
,
2
,
3
,
…
,
15
}
\xi = \{1, 2, 3, \ldots, 15\}
ξ
=
{
1
,
2
,
3
,
…
,
15
}
A
=
{
multiples of
3
}
A = \{\text{multiples of }3\}
A
=
{
multiples of
3
}
B
=
{
factors of
15
}
B = \{\text{factors of }15\}
B
=
{
factors of
15
}
(a)
List the members of
A
∩
B
A \cap B
A
∩
B
.
(b)
Find
n
(
A
∪
B
)
n(A \cup B)
n
(
A
∪
B
)
.
(c)
Ali says that
n
(
A
∪
B
)
n(A \cup B)
n
(
A
∪
B
)
can always be worked out as
n
(
A
)
+
n
(
B
)
n(A) + n(B)
n
(
A
)
+
n
(
B
)
.
Explain why Ali is wrong.
●●●
●●
Level 3
4 marks
Start
→
Probability from Venn diagrams
12 questions
Lesson
Not started
Mark as done
50
50
50
people were asked whether they had visited France (
F
F
F
) or Spain (
S
S
S
).
28
28
28
had visited France,
24
24
24
had visited Spain, and
6
6
6
had visited neither.
(a)
Work out how many people had visited both France and Spain. (2 marks)
(b)
One of the
50
50
50
people is chosen at random. Work out the probability that they had visited France but not Spain. (1 mark)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
40
40
40
people were asked whether they drink tea (
T
T
T
) and whether they drink coffee (
C
C
C
).
The Venn diagram shows the results.
ξ
9
T
C
13
9
9
One of the
40
40
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 marks
Start
→
Mark as done
50
50
50
people were asked whether they read a newspaper (
N
N
N
) and whether they listen to the radio (
R
R
R
). The Venn diagram shows the results.
ξ
9
N
R
22
8
11
One of the
50
50
50
people is chosen at random.
(a)
Find
P
(
N
∪
R
)
P(N \cup R)
P
(
N
∪
R
)
.
(b)
Find
P
(
N
′
)
P(N')
P
(
N
′
)
.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
The Venn diagram shows the probabilities for two events
A
A
A
and
B
B
B
.
ξ
0.3
A
B
0.35
0.2
0.15
(a)
Find
P
(
A
)
P(A)
P
(
A
)
.
(b)
Find
P
(
A
∪
B
)
P(A \cup B)
P
(
A
∪
B
)
.
(c)
Find
P
(
B
′
)
P(B')
P
(
B
′
)
.
●●●
●●
Level 3
6 marks
Start
→
Mark as done
80
80
80
students were asked whether they play a musical instrument (
M
M
M
) and whether they are in a sports team (
S
S
S
). The Venn diagram shows the results.
ξ
21
M
S
27
18
14
One of the
80
80
80
students is chosen at random.
(a)
Find
P
(
M
∪
S
)
P(M \cup S)
P
(
M
∪
S
)
.
(b)
Kai works out
P
(
M
∪
S
)
P(M \cup S)
P
(
M
∪
S
)
by adding
P
(
M
)
P(M)
P
(
M
)
and
P
(
S
)
P(S)
P
(
S
)
together. Explain why Kai's method gives an answer that is too large.
●●●
●●
Level 3
3 marks
Start
→