Correct Answer - D
The set A has n elements. So, it has
2
n
2
subsets.
Therefore, set P can be chosen in
2
n
C
1
2
ways. Similarly, set Q can also be chosen in
2
n
C
1
2
ways.
∴
∴
Sets P and Q can be chosen in
.
2
n
C
1
×
.
2
n
C
1
=
2
n
×
2
n
=
4
n
.
ways.
If P contains r elements, then Q must contain (r+1) elements.
In this case the number of ways of choosing P and Q is
.
n
C
r
×
.
n
C
r
+
1
.
, where
0
≤
r
≤
n
−
1
0
.
Thus, the number of ways of choosing P and Q in general, is
n
−
1
∑
r
=
0
.
n
C
r
×
.
n
C
r
+
1
=
.
2
n
C
n
−
1
∑
Hence, required probability
=
.
2
n
C
n
−
1
4
n
=