Suppose that for a recent admissions class, an St Peter College received 4,442 applications for early admission. Of this group, it admitted 2533 students early, rejected 1035 outright and deferred 874 to the regular admission pool for further consideration. In the past, this school has admitted 23% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 3975. Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. a. Use the data to estimate P(E), P(R), and P(D). (2 marks) b. Are events E and D mutually exclusive? Find P(ED). (1 marks) c. For the 3975 students who were admitted, what is the probability that a randomly selected student was accepted during early admission? (1 mark) d. Suppose a student applies for early admis