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 admisiion 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 admissions is admitted early, rejected outright, or deferred to the regular admissions pool. A) Use data to estimate P(E), P(R), and P(D). B) Are events E and D mutually exclusive? Find P(EUD). C) For the 2375 students who were admitted, what is the probability that a randomly selected student was accepted during early admission? D) SUppose a student applies for early admission. What is the probability that the students will be admitted for early admission or be deferred and later admitted during the regular admission process?

Answer 1

Solution:-

Given that

From the given information, we have

Let E, R and D represent the events that a student who applies for early admission is admitted early, rejected couright and deferred to the regular admissions pool.

Total number of application is 2851.

a) Use data to estimate P(E), P(R) and P(D).

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

From the given information, the events E and D are mutually exclusive, because only one event can occur at a time.

Here,

The Events E and D are mutually exclusive events.

So, P(E U D) = 0.36 + 0.34

= 0.7

c) For the students who were admitted, what is the probability that a randomly selected student was accepted during early admission?

The probability that a randomly selected student was accepted for early admission is,

P(Accepted for early admission) =

= 0.4349

Therefore The probability that a random selected student was accepted for early admission is 0.4349

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

The probability that the students will be admitted for early admission or be deferred and later admitted during the regular admission process is,

P(Early admissions or regular admission pool

= {P(E) + P(D) x P (regular admission pool)}

= 0.36 + 0.34 (0.18)

= 0.4212

The probability that the students will be admitted for early admission or be deferred and later admitted during the regular admission process is 0.4212.

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