Correct Answer - A
The set A has n elements. So, it has
2
n
subsets.
Therefore, set P can be chosen in
2
n
C
1
ways. Similarly, set Q can also be chosen in
2
n
C
1
ways.
∴
Sets P and Q can be chosen in
.
2
n
C
1
×
.
2
n
C
1
=
2
n
×
2
n
=
4
n
ways.
The total number of ways of selecting P and Q such that P=Q, is
n
∑
r
=
0
.
n
C
r
=
2
n
Hence, required probability
=
2
n
4
n
=
1
2
n
ALITER If P=Q, then each element can be listed in two ways (i), (ii) only.
∴
Favourable number of elementary events
=
2
n
Hence, required probability
=
2
n
4
n