A number x is selected at random in the interval [−1, 2]. Let the events A = {x < 0}, B = {|x − 0.5| < 0.5}, and C = {x > 0.75}. (a) Find the probabilities of A, B, A \cap B, and A \cap C. (b) Find the probabilities of A\cup B, A\cup C, and A\cup B\cup C, first, by directly evaluating the sets and then their probabilities, and second, by using the appropriate axioms or corollaries.