Question

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.(a) Use the data to estimate P(E ), P(R), and P(D). If required, round your answers to four decimal places.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.

Answer 1

Answer:

a. P(E) = 1033/ 2851=0.3623

P(R) = 854/2851=0.2995

P(D) = 964/2851=0.3381

P(E ∩ D) = P(E) +P(D)= 0.3623 +0.3381= 0.7004

(d)  0.423 158

Step-by-step explanation:

a. P(E) = 1033/ 2851=0.3623

P(R) = 854/2851=0.2995

P(D) = 964/2851=0.3381

(b) Are events E and D mutually exclusive?

Yes these events are mutually exclusive. If students are deferred they may be admitted later but not early.  Mutually Exclusive or disjoint events do not occur at the same time.

P(E ∩ D) = P(E) +P(D)= 0.3623 +0.3381= 0.7004

(c) For the 2,375 students who were admitted,  the probability that a randomly selected student was accepted during early admission is

P(E) = 1033/ 2851=0.3623

P(E) + P(D for later admission)  =0.3623 + 18%*0.3381

                                                    =0.3623 + 0.0609 = 0.423 158