Brown University received 2851 applications for early admission. Of this group i

Question

Brown University received 2851 applications for early admission. Of this group it admitted 1033 students early, rejected 854 students outright, and deferred 964 to the regular admission pool for further consideration. Historically. Brown has admitted 18% of the deferred early admission applicants from the regular admission pool. The total number of students admitted was 2375 (include students admitted through early admission and the regular admission pool). Let E = event that a student who applied for early admission is admitted early. Let R event that a student who applied for early admission is rejected outright. Let D = event that at student who applied for early admission is deferred to the regular admission pool. (a) Calculate P(E), P(R) and P(D). (b) Arc the events E and D mutually exclusive? Briefly explain (c) Find P(E D). (d) For the 2375 students who were admitted, what is the probability that a randomly selected student was accepted during early admission. (e) 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?

Explanation / Answer

a) P(E) =1033/2851

P(R)=854/2851

P(D) =961/2851

b) Yes, as they do not contain any common student in their respective sample space,

c) P(EnD) =0; as there are no common element.,

d) probabilty =1033/2375

e)required probabilty =probabilty of early admiision +probabilty of being deffered and then admitted

=(1033/2851)+(964/2851)*0.18 =0.4232

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