Suppose that at any sitting of EC 16A, 30% of the students are first year; 35% are second year; 20% are final year and 15% are qualifying to enter various programmes (assume mutually exclusive). From records of the Statistics department, it was found that 20% of the first year students get A; 30% of the second year students get A; 35% of the final year students get A; 25% of the qualifying students get A. What is the probability a randomly chosen student will get an A? Given that a student got an A, what is the probability the student was first year? Second year? Third year? Qualifying