S is a set containing n elements. If two subsets A and B of S picked at random from the set of all subsets of S. Then the probability that A and B have no common element.

if a set having 'x' is a element selected sub set which are. 

                                                             A             B  

A, B both no common                     {  }           {  }

elements 'B' cases                          {  }           {x}  

Probability $=\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$                          {x}           {  }

for 'n'  elements $={\left(\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\right)}^{\mathrm{n}}$           {x}           {x}