Question

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 $E, R,$ 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. $$egin{array}{l}{ ext { a. Use the data to estimate } P(E), P(R), ext { and } P(D) ext { . }} \ { ext { b. Are events } E ext { and } D ext { mutually exclusive? Find } P(E cap D) ext { . }}end{array}$$ $egin{array}{l}{ ext { c. For the } 2375 ext { students that were admitted, what is the probability that a randomly }} \ { ext { selected student was accepted during early admission? }}end{array}$ d. 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?

          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 $E, R,$ 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.
$$egin{array}{l}{	ext { a. Use the data to estimate } P(E), P(R), 	ext { and } P(D) 	ext { . }} \ {	ext { b. Are events } E 	ext { and } D 	ext { mutually exclusive? Find } P(E cap D) 	ext { . }}end{array}$$
$egin{array}{l}{	ext { c. For the } 2375 	ext { students that were admitted, what is the probability that a randomly }} \ {	ext { selected student was accepted during early admission? }}end{array}$
d. 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?

Added by Patrick P.

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