made easy test series

Question

Consider ‘A’ is a set containing n elements. A subset ‘P’ of ‘A’ is chosen at random. The set ‘A’ is reconstructed by replacing the elements of ‘A’. A subset ‘Q’ of ‘A’ is again chosen at random. What is the probability that ‘P’ and ‘Q’ have no common element?

Comments

$\frac{\binom{n}{0} . 2^{n} + \binom{n}{1} . 2^{n-1}+\binom{n}{2} . 2^{n-2} +..... +\binom{n}{n} . 2^{0} - 1 }{2^{n} }$

i am not able to simplify further