Mathematics · Oct / Nov 2024 · Paper 61 · Question 3
YMA01
As printed in the paper
The question as text
3. A group of 200 adults were asked whether they read cooking magazines, travel magazines or sport magazines. Their replies showed that • 29 read only cooking magazines • 33 read only travel magazines • 42 read only sport magazines • 17 read cooking magazines and sport magazines but not travel magazines • 11 read travel magazines and sport magazines but not cooking magazines • 22 read cooking magazines and travel magazines but not sport magazines • 32 do not read cooking magazines, travel magazines or sport magazines
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
3(a)[3]
'14'
3(b)(i)[1]
200
'33' '11' '42' '32'
+
+
+
118
or 200
−
'29' '22' '14' '17'
−
−
−
118
3(b)(ii)[2]
=
=
200
200
200
200
'14' '11'
+
25
3(c)[2]
=
'14' '11' '22' '33'
+
+
+
80
Notes
For a fully correct Venn diagram
(B2 for at least 6 numbers in the correct place on the Venn diagram)
(B1 for at least 3 numbers in the correct place on the Venn diagram)
(a)
B3
Treat blanks on the diagram as zero
Condone correct probabilities instead of frequencies e.g. 22 200 oe or 0.11 as 22
For '14'
(b) (i)
B1ft
200 oe ft their Venn diagram
'33' '11' '42' '32'
+
+
+
or 200
−
'29' '22' '14' '17'
−
−
−
ft their Venn diagram. May be implied
200
200
(ii)
M1
by 118
oe
200
For 118
A1
oe
200
n
'14' '11' '22' '33'
' '
n provided 0 < n < 80
+
+
+
provided the answer gives a probability
80
and 0 < n < 80
ft the Venn diagram for numerator
(c)
M1
ft the Venn diagram for the denominator
or '
'
m where 0 < m < 0.4
m
0.4
or '0.4'
where 0 < m < 0.4
ft the Venn diagram for numerator
ft the Venn diagram for the denominator
For 25
A1
oe Allow 0.313
80
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