[ig06]

Here is my solution:
Number of possible combinations of subsets A and B = (2^n)*(2^n)=4^n since A and B are chosen independently and there are 2^n possible subsets.

Number of ways that A can be a subset of B is

Subset_tot=sum from k=0 to n of C(k,n)*2^k

since for there are C(k,n) possible subsets B with k elements and 2^k possible subsets of each of those (the sum C(i,k) from i=0 to k is 2^k).

Noting that the sum from k=0 to n of C(k,n)*r^k is (1+r)^n

Subset_tot=3^n

So there are 3^n ways A can be a subset of B and 4^n ways of picking A and B in total so
Prob(A is a subset of B)=3^n/4^n=(3/4)^n