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.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?

Answer 1

Answer:

0.423

Step-by-step explanation:

E represents the event that student who applied for early admission is admitted early.

Out of 2851 applicants of early admissions, 1033 students were admitted early, so probability that a student gets early admssion is = P(E) = $\frac{1033}{2851}$

Similarly, R represents the event that the student is rejected. So probability that the student is rejected is = P(R) = $\frac{854}{2851}$

D denotes the event that student is deferred. Since 964 students are deferred, probability that a student is deferred is = P(D) = $\frac{964}{2851}$

Only 18% of the deferred early admissions get admission in regular session. Let R be the event that student gets admission during regular admission process. So, the probability that a deferred student gets admission in regular session is = P(D ∩ R) = $0.18 \times \frac{964}{2851}=\frac{4338}{71275}$

We need to find:

The probability that the student will be admitted for early admission OR be deferred and later admitted during the regular admission process.

i.e. we need to find: P(E) OR P(D ∩ R)

Using the values of the probabilities we get:

P(E) OR P(D ∩ R) = P(E) + P(D ∩ R) = 0.423 (rounded to 3 decimal places)

Answer 2

The probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process is 0.423.

What is Probability?

This is defined as the numerical descriptions of how likely an event is to occur.

Parameters

The probability that a student gets early admission is = P(E) = 1033/2851

The probability that the student is rejected is = P(R) = 854/2851

The probability that a student is deferred is = P(D) = 964/2851

Let R be the event that student gets admission during regular admission process.

The probability that a deferred student gets admission in regular session is = P(D ∩ R) = 0.18 × 964/2851

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

P(E) OR P(D ∩ R

P(E) OR P(D ∩ R) = P(E) + P(D ∩ R) = 0.423.

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