Answer all questions with explanation

3)(32 points - 24 minutes) The express mail to a large Boston corporation is delivered by three firms: Fad Express, Pereolator, and USP. Based on recent corporate data, 40 percent of the deliveries are made by Fad Express, 10 percent by Percolator, and 50 percent by USP. Even though all three companies guaranteed delivery by 11 A.M., 15 percent of Fad Express' deliveries are late (i.e., arrive after 11 A.M.}, and 30 percent of USP's deliveries are late. a) If the probability that an express mail delivery arrives late at this corporation is 0.25, what is the probability that a Percolator delivery is late? b) Are the events that a delivery arrives late and that a delivery is made by Percolator independent? c) Given that an express mail delivery arrives late at this corporation, what is the probability that USP delivered it? d) Given that an express mail delivery arrives on time at this corporation, what is the probability that Fad Express did not deliver it