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Manipal Entrance Test 2015 Math Paper
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© examsnet.com
Question : 8
Total: 70
Let
X
denotes the number of times heads occur in
n
tosses of a fair coin. If
P
(
X
=
4
)
,
P
(
X
=
5
)
and
P
(
X
=
6
)
are in
A
P
,
then the value of
n
is
7
,
14
10
,
14
12
,
7
14
,
12
Validate
Solution:
Clearly,
X
is a binomial variate with parametres
n
and
p
=
1
2
such that
P
(
X
=
r
)
=
n
C
r
p
r
q
n
−
r
=
n
C
r
(
1
2
)
r
(
1
2
)
n
−
r
=
n
C
r
(
1
2
)
n
Now,
P
(
X
=
4
)
,
P
(
X
=
5
)
and
P
(
X
=
6
)
are in
A
P
.
⇒
2
P
(
X
=
5
)
=
P
(
X
=
4
)
+
P
(
X
=
6
)
⇒
2
.
n
C
5
(
1
2
)
n
=
n
C
4
(
1
2
)
n
+
n
C
6
(
1
2
)
n
⇒
2
.
n
C
5
=
n
C
4
+
n
C
6
⇒
2
.
n
!
(
n
−
5
)
!
5
!
=
n
!
(
n
−
4
)
!
4
!
+
n
!
(
n
−
6
)
!
6
!
⇒
2
5
(
n
−
5
)
=
1
(
n
−
4
)
(
n
−
5
)
+
1
6
×
5
⇒
n
2
−
21
n
+
98
=
0
⇒
(
n
−
7
)
(
n
−
14
)
=
0
∴
n
=
7
or 14
© examsnet.com
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