Mathematics · Oct / Nov 2024 · Paper 61 · Question 7
YMA01
As printed in the paper
The question as text
7. A box contains only red counters and black counters. There are n red counters and n + 1 black counters. Two counters are selected at random, one at a time without replacement, from the box.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
7(a)[3]
Black
1
2
1
+
1
n
Red
n
2
n +
1
on the tree diagram
2
n
n
2
Red
n
1
+ in the correct places on
1
+
1
n
− and
n
n
Black
2
2
2
n
+
1
n
n
the tree diagram
n
Black
n
n
and
in the correct places on the
2
n
2
2
n
n
tree diagram
+
1
+
1
n
n
n
n
7(b)[2]
'
' '
×
' '
+
' '
×
'
2
n
+
1
2
n
2
n
+
1
2
n
= 2 (
1)
1
n n
+
n
+
=
+ *
2 (2
+
1)
2
1
n
n
n
1
25
n
+
7(c)[2]
=
=
24
So 49 counters in the box
n
2
+
1
49
n
25
24
'
' '
×
'
1
49
48
7(d)[2]
=
25
2
49
Notes
+
1
n
n
(a)
B1
For 2
and
in the correct places on the tree diagram
n +
1
2
n
+
1
− and
1
+ in the correct places on the tree diagram
1
n
n
B1
For
2
2
n
n
n
n
in the correct places on the tree diagram . Allow 1
n
B1
For
and
for
in both places
2
2
2
2
n
n
n
(b)
M1
For use of P(Red) × P(Black) + P(Black) × P(Red) ft their tree diagram
Answer is given so no incorrect working can be seen. Must have at least one correct line of
A1*
working between M1 and the given answer.
(c)
M1
For solving to find n = 24
A1
Cao
For a correct ratio ft their n and their tree diagram
n
+
1
n
×
(d)
M1
Allow a correct ratio in terms of n e.g.
2
1
2
oe ft their tree diagram for the numerator
n
+
n
n
+
1
2
n
+
1
A1
For 0.5 (Working must be seen)
162
−
μ
= −
1.2816
(Calculator gives –1.28155…)
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