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, rejected 854 outright, and deferred 964 to the regular admissions pool. Penn admitted about 18% of the applicants in the regular admissions pool for a total class size (number of early admissions plus number of regular admissions) of 2375 students (USA Today, January 24, 2001). Let E, R, and D represent the events that a student who applies for early admission is admitted, rejected outright, or deferred to the regular admissions pool; and let A represent the event that a student in the regular admissions pool is admitted.

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 accepted for admission in the regular admissions pool?