Correct Answer - B
The set A has 2n
elements. Therefore, two subsets P and Q can be chosen in 2nC2
ways.
Suppose P consists of r elements. Then, P can be chosen in .nCr
.
Since, Q=
ˉ
P
. Therefore, P and Q can be chosen in .nCr
ways. But, r can vary from 0 to n and P and Q can be interchanged also.
∴
Number of ways of selecting P and Q such that Q=
ˉ
P
is
1
2
n
∑
r=0
.nCr=2n-1
Hence, required probability =
2n-1
.2nC2
=
1
2n-1