Question

In fall 2014, 32% of applicants with a Math SAT of 700 or more were admitted by a certain university, while 12% with a Math SAT of less than 700 were admitted. Further, 34% of all applicants had a Math SAT score of 700 or more. What percentage of admitted applicants had a Math SAT of 700 or more? (Round your answer to the nearest percentage point.)

Answer 1

Let us define the following events:

A: an applicant has a Math SAT score of 700 or more

=> Ac: an applicant has a Math SAT score of less than 700

X: an applicant is admitted by the university.

Now, we are given that "32% of applicants with a Math SAT of 700 or more were admitted by a certain university", which means that:

P(X|A) = 32% = 0.32

Moreover, we are given that "12% with a Math SAT of less than 700 were admitted", which means that:
P(X|Ac) = 12% = 0.12

Moreover, we are given that "34% of all applicants had a Math SAT score of 700 or more", which means that:

P(A) = 34% = 0.34

=> P(Ac) = 1 - P(A) = 1 - 0.34 = 0.66

Now, the percentage of admitted applicants who had a Math SAT of 700 or more is given by:

For any queries, feel free to comment and ask.

If the solution was helpful to you, don't forget to upvote it by clicking on the 'thumbs up' button.