Roll a fair six-sided die three times. Let A1 = {1 or 2 on the first roll}, A2 = {3 or 4 on the second roll}, and A3 = {5 or 6 on the third roll}. It is given that P(Ai) = 1/3, i = 1, 2, 3; P(Ai ∩ Aj) = (1/3)2, i = j; and P(A1 ∩ A2 ∩ A3) = (1/3)3. (a) Use Theorem 1.1-6 to find P(A1 ∪ A2 ∪ A3). (b) Show that P(A1 ∪ A2 ∪ A3) = 1 − (1 − 1/3)3.