T.C.Fox, marketing director for Metro-Goldmine Motion Pictures, believes that the studio's upcoming release has a 60 percent chance of being a hit, a 25 percent chance of being a moderate success, and a 15 percent chance of being a flop. To test the accuracy of his opinion, T.C. has scheduled two test screenings. After each screening, the audience rates the film on a scale of 1 to 10, 10 being the best. From his long experience in the industry, T.C. knows that 60 percent of the time, a hit picture will receive a rating of 7 or higher; 30 percent of the time, it will receive a rating of 4, 5, or 6; and 10 percent of the time, it will receive a rating of 3 or lower. For a moderately successful picture, the respective probabilities are 0.30, 0.45, and 0.25; for a flop, the respective probabilities are 0.15, 0.35, and 0.50.
(a) If the first test screening produces a score of 6, what is the probability that the film will be a hit?
(b) If the first test screening produces a score of 6 and the second screening yields a score of 2, what is the probability that the film will be a flop (assuming that the screening results are independent of each other)?