Mathematics · Oct / Nov 2025 · Paper 61 · Question 3
YMA01
As printed in the paper
The question as text
3. A fair 6-sided die is rolled. The random variable Y represents the score on the uppermost face.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
3(a)[2]
P
Y
=
y
=
[ y = ] 1, 2, 3, 4, 5, 6
6
3(b)[1]
[Discrete] uniform [distribution]
+
6 1
( )
E
Y
=
[ 3.5]
=
or
2
3(c)[3]
4Y + 3 : 7, 11, 15, 19, 23, 27
1
+
2
+ +
3
4
+ +
5
6
( )
=
=
E
Y
[ 3.5]
6
+
"7" "27"
or
E(4
Y
+
3)
=
2
E(4
Y +
3)
=
4 "3.5" 3
×
+
+
+
+
+
+
"7" "11" "15" "19" "23" "27"
6
17
1
for identifying (
)
P
Y
=
y
=
as the only probability
6
(a)
B1
Ignore labels. (May be seen in a table). Must be seen in part (a).
Stating or using Normal, Binomial (or other distribution) is B0
Dep on previous B1 for y = 1, 2, 3, 4, 5, 6 Ignore labels. (May be seen
dB1
in a table) Must be seen in part (a).
Use of inaccurate value for 1
6 can score B0B1 if otherwise fully
SC
e.g.
1
2
3
4
5
6
0.167
0.167
0.167
0.167
0.167
0.167
do not allow continuous uniform [distribution] do not allow Normal
(b)
B1
uniform
a correct method to find E(Y) (implied by 3.5)
or sight of 7, 11, 15, 19, 23, 27 (allow one slip)
(c)
M1
1
2
3
4
5
6
is M0
1
×
+ ×
2
+ ×
3
+ ×
4
+ ×
5
+ ×
6
6
6
6
6
6
6
use of 4E( )
Y + ft their E( )
Y must be clear that they are using their
3
E(Y)
M1
1
+
e.g.
is M0
4
3
6
or a correct method to find E(4Y + 3) ft their 7, 11, 15, 19, 23, 27
A1
cao 17 scores 3/3
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