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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 2,851 applications for early admission. Of this group, it admitted 1,033 students early, rejected 854 outright, and deferred 964 to the regular admissions 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. If your answer is zero, enter "0". a. Use the data to estimate P(E), P(R), and P(D) (to 4 decimals). P(E) 1033 P(R) P(D) 964 b. Are events E and D mutually exclusive? 854 -Select your answer. Find P(END) (to 4 decimals). 0.439 c. For the 2,375 students who were admitted, what is the probability that a randomly selected student was accepted for early admission (to 4 decimals)? 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 (to 4 decimals)?

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 2,851 applications for early admission. Of this group, it admitted 1,033 students early, rejected 854 outright, and deferred 964 to the regular admissions 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. If your answer is zero, enter "0". a. Use the data to estimate P(E), P(R), and P(D) (to 4 decimals). P(E) 1033 P(R) P(D) 964 b. Are events E and D mutually exclusive? 854 -Select your answer. Find P(END) (to 4 decimals). 0.439 c. For the 2,375 students who were admitted, what is the probability that a randomly selected student was accepted for early admission (to 4 decimals)? 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 (to 4 decimals)?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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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 2,851 applications for early admission. Of this group, it admitted 1,033 students early, rejected 854 outright, and deferred 964 to the regular admissions 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. If your answer is zero, enter "0". a. Use the data to estimate P(E), P(R), and P(D) (to 4 decimals). P(E) P(R) 854 P(D) 964 b. Are events E and D mutually exclusive? - Select your answer Find P(En D) (to 4 decimals). 1033 0.439 c. For the 2,375 students who were admitted, what is the probability that a randomly selected student was accepted for early admission (to 4 decimals)? 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 (to 4 decimals)?
Transcribed Image Text: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 2,851 applications for early admission. Of this group, it admitted 1,033 students early, rejected 854 outright, and deferred 964 to the regular admissions 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. If your answer is zero, enter "0". a. Use the data to estimate P(E), P(R), and P(D) (to 4 decimals). P(E) P(R) 854 P(D) 964 b. Are events E and D mutually exclusive? - Select your answer Find P(En D) (to 4 decimals). 1033 0.439 c. For the 2,375 students who were admitted, what is the probability that a randomly selected student was accepted for early admission (to 4 decimals)? 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 (to 4 decimals)?
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