Suppose that for a recent admissions class, an Ivy League college received 2,851 applications for early admission. Of this group

Question

9 days ago

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Suppose that for a recent admissions class, an Ivy League college received 2,851 applications for early admission. Of this group

, it admitted 1,033 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 2,375. 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.
Use the data to estimate P(E ), P(R), and P(D). If required, round your answers to four decimal places.

(a)

P(E) =

P(R) =

P(D) =

(b) Are events E and D mutually exclusive? Find P(E ∩ D). If your answer is zero, enter "0".

(c) For the 2,375 students who were admitted, what is the probability that a randomly selected student was accepted during early admission? If required, round your answer to four decimal places.

(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? If required, round your answer to four decimal places.

Mathematics

1 answer:

Zina [12.3K] · Answer 1 · 2026-04-07T03:54:30+03:00

A) Probability is a measure of how likely an event will happen. Here, we calculate the probability of X as: P(X) = X/N, where X is the successful outcomes, and N is the total outcomes. P(E) = E/N = 1033/2851 = 0.3623 P(R) = R/N = 854/2851 = 0.2995 P(D) = D/N = 964/2851 = 0.3381 B) Events E and D are mutually exclusive since students accepted early can't be deferred to the regular admission pool, hence, intersection P(E ∩ D) is 0. C) The count of early accepted students is 1033, and the overall accepted students are 2375. Thus, the probability is: P = 1033/2375 = 0.4349 D) Reformulating the question: What’s the probability of being accepted if applying for early admission? Given that 18% of deferred students ultimately got accepted, 0.18 × 964 = 174 was admitted later. Thus, the probability of being deferred and then accepted becomes: P(DA) = 174/2831 = 0.0610. The chance of randomly selecting a student early accepted or deferred then accepted is: P(E or DA) = 0.0610 + 0.3623 = 0.4233, applying the addition rule.