high school seniors with strong academic records apply to the nation’s most sele
ID: 3044331 • Letter: H
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.A- use the data to estimate P(E), P(R), and P(D).
B- Are events E and D mutually exclusive? Find P(E D).
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 student will be admitted for early admission or be deferred and later admitted during the regular admission process?
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.
A- use the data to estimate P(E), P(R), and P(D).
B- Are events E and D mutually exclusive? Find P(E D).
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 student will be admitted for early admission or be deferred and later admitted during the regular admission process?
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.
A- use the data to estimate P(E), P(R), and P(D).
B- Are events E and D mutually exclusive? Find P(E D).
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 student will be admitted for early admission or be deferred and later admitted during the regular admission process? A- use the data to estimate P(E), P(R), and P(D).
B- Are events E and D mutually exclusive? Find P(E D).
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 student will be admitted for early admission or be deferred and later admitted during the regular admission process? 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 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 = 0.3623
b)
E - early admission
D - Deferred
Both are mutually exclusive, because a student can be admitted early or deferred.
A deferred student who will be admitted later will not form the set of early admission set.
therefore P (E intersection D) = 0
c)
totally 2375 students of which early admisssions were 1033
P (early admission) = 1033/2375 = 0.4349
d)
probabilty (early admission) = 0.36
probability (admission after being deferred) = 0.33*0.18=0.0608
Therefore
probabilty (early admission or admission after being deferred) = 0.3600+0.0608=0.4208
probability applications 2851 early admissions (E) 1033 0.3623 rejections (R) 854 0.2995 deferred (D) 964 0.3381Related Questions
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