1. (6 points) Suppose that we have the following information P(A) = 0.5, P(B) = 0.6, and P(AU B) = 0.8. 1) (2 points) Find the probabilities P(An B) and P(Acn BC) 2) (2 points) Whether or not A and B are independent and explain why. 3) (2 points) Find the probabilities P(A | B) and P(A | B"). 2. (6 points) You roll two fair six-faced dice both with equally likely outcomes from the set { 1, 2, 3, 4, 5, 6}. 1) (2 points) Find the probability, denoted by P(D2), that the absolute value of the difference of the two dice is 2. 2) (2 points) Find the probability P(As) that the sum of the two dice is 6. 3) (2 points) Find the probability P(M12) that the product of the two dice is 12