A set contains n elements. a sub set P of A is chosen, the set  is reconstructed by replacing the elements of P. A subset Q of A is again chosen , the no of ways of chosing P n Q so that intersection of P n Q is phi

Every element x of the given set has four chances,They are

1)xP,xQ     2)xP,x doesnot belong to Q

3)x does not belong to P,xQ  4)x does not belong to both P,Q.

For PQ to be ,the conditions 2,3,4 are favourable while 1 is not bcoz if x belongs to both sets,Their intersection can't be .So,the required probability is (3/4)ⁿ

Alter method;

The no.of subsets for a set with n elements is 2ⁿ.Let us select r elements from the set in nc_r ways to form the set P.Since PQ=,the subset Q can be selected only from the subsets formed by remaining (n-r) elements which are 2^n-r.Hence the total no.of ways are

nc_r.2^n-r=3ⁿ.Hence the probability is 3ⁿ/2ⁿ.2ⁿ=(3/4)ⁿ