One of the 256 subsets of {1, 2, 3, 4, 5, 6, 7, 8} is chosen uniformly at random. Let X be the number of elements of this subset. Let Y be 1 if the subset is empty and be the least element of the subset otherwise.
(i) Are the events "X = 1" and "Y = 3" independent?
(ii) Are the random variables X and Y independent?
(iii) What is Pr(X <= 2 | Y <= 5)?
