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. Suppose that
for a recent admissions class, an Ivy League college received 2851 applications for
early admission. Of this group, it admitted 1033 students early, rejected 854
outright, and deferred 964 to the regular admission pool for further consideration.
In the past, this school has admitted 18% 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 2375. Let ?, ?, and ? represent the events that a student who applies for early
admission is admitted early, rejected outright, or deferred to the regular
admissions pool.
a. Are events E and D mutually exclusive? Find (? ∩ ?)
b. Suppose a student applies for early admission. What is the probability that
the student will be admitted for early admission or be deferred and later
admitted during the regular admission process?