29. High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. The University of Pennsylvania received 2851 applications for early admission. Of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admissions pool for further consideration. In the past, Penn has admitted about 18% of the deferred early admission applicants during the regular admission process. Counting the additional students who were admitted during the regular admission process, the total class size was 2375 (USA Today,January 24, 2001).

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).

b. Are events E and D mutually exclusive? Find P(E  D).

c. For the 2375 students admitted to Penn, what is the probability that a randomly selected student was accepted for early admission?

d. Suppose a student applies to Penn for early admission. What is the probability the student will be admitted for early admission or be deferred and later admitted during the regular admission process?