CONSIDER THE EVENTS DONATED BELOW!!!!!!!!

(24 pts) Consider three events denoted T, H, and M. Suppose M and T are independent, and that: P[T] = 0.3, P[H] = 0.5, P[M] = 0.5, P[T ~ H] = 0.2 (a) What is the probability that M occurs and at the same time T does not? (b) What is the probability that either T occurs or H occurs, but not both? (c) What is the probability that T occurs given that H was observed not to occur? (24 pts) A mathematics class for engineers has 25 civil engineering students and 55 mechanical engineering students. Based on past observations, the probability that a civil engineering student will fail the course is 6%, while the probability that a mechanical engineering student will fail is 14%. (a) What is the total probability that a student will fail the math class? (b) Given that an individual failed the course last semester, what is that probability that he or she is a civil engineering student? (c) If 10 students are randomly selected, what is the probability that exactly 3 are civil engineering students? (12 pts) In simple frame structures (with rigid floors), the total deformation of the top story Y is given by the following function of the deformations of the individual stories: Y = 1.20X1 + 1.10X2 Suppose E[Xi] = 2.4 inches with Var[Xi] = 2.0 in', and E[X2] = 3.0 inches with Var[X2] = 3.0 in. Assuming that X1 and X2 are independent, what are the mean and standard deviation of Y