Algebra 2 - Probability

Question

On average, a very selective college admits 9 out of every 100 applicants. An admissions officer is reviewing a pile of 200 students' applications, and admits the first 17 students.

What are the chances that she will admit the 18th student?


100%
9%
17%
0%

Answer 1

Hi Summer D.,

The important thing to bear in mind here is that 9/100 is the average admission rate for the college. Unless you had specific information that the college will only admit 18 students total in the admitting class (such a college would soon be out of business!), that 9/100 is the probability you must apply to all successive picks, no matter what the "admitted" pile is. So, 9%.

Of course, if you looked at it another way, you could say that the 9% figure only applies until the admission officer starts considering the application, and totes up the "points". And maybe not even then, because the college MIGHT construct a histogram and then choose a cutoff so as to exactly fill their dormitory, etc. Or, if you knew the data on the application, and what the college's rating system favored, YOU would know definitely. And so on.

-- Cheers, Mr. d.