Correct Answer - A
We,have
p= Probability of getting an even number in a throw
⇒
p
=
3
6
=
1
2
⇒
∴
q
=
1
−
p
=
1
2
∴
Let X denote the number of times an even number is shown in
(
2
n
+
1
)
(
throws of a dice. Then, X follows binomial distribution such that
P
(
X
=
r
)
=
.
2
n
+
1
C
r
(
1
2
)
2
n
+
1
−
r
(
1
2
)
r
=
.
2
n
+
1
C
r
(
1
2
)
2
n
+
1
P
.
∴
∴
Required Probability
=
2
n
+
1
∑
r
=
1
P
(
X
=
r
)
=
2
n
+
1
∑
r
=
1
2
n
+
1
.
C
_
r
(
1
2
)
2
n
+
1
=
=
(
1
2
)
2
n
+
1
{
.
2
n
+
1
C
1
+
.
2
n
+
1
C
3
+
...
.
.
+
.
2
n
+
1
C
2
n
+
1
}
=
=
1
2
2
n
+
1
×
2
2
n
=
1
2
=
.
