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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)?