2. Now do the same as above in the following situation: Suppose now that first a fair coin is tossed. If the outcome is 1, then a biased coin that gives 0 with probability 1/4 and 1 with probability 3/4 is tossed. If the outcome of the fair coin toss is 0, then another biased coin, one that gives 0 with probability 1/3 and 1 with probability 2/3. Suppose we are only interested in the outcomes, so let again be {(0, 0), (0, 1), (1, 0), (1, 1)}, and compute the same things for this situation:

(a) What is the probability measure Pr on the elements of ?

(b) Are X and Y independent?

(c) Let again Z be the XOR of X and Y. Are now Y and Z independent?