AIME II Problem 10 2007

[zefuri]

Let S be a set with six elements. Let P be the set of all subsets of S. Subsets A and B of S, not necessarily distinct, are chosen independently and at random from P. the probability that B is contained in at least one of A or S-A is [unparseable or potentially dangerous latex formula], where m, n, and r are positive integers, n is prime, and m and n are relatively prime. Find m+n+r. (The set S-A is the set of all elements of S which are not in A.)