Question

In fall 2014, 34% of applicants with a Math SAT of 700 or more were admitted by a certain university, while 16% with a Math SAT of less than 700 were admitted. Further, 38% 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

Answer: Our required percentage would be 57%.

Step-by-step explanation:

Since we have given that

Probability of applicants with a Math SAT of 700 or more were admitted = 34%= P(A|E)= 0.34

Probability of applicants with a Math SAT of less than 700 were admitted = 16% = 0.16 = P(A|E')

Probability of all applicants had a Math SAT score of 700 or more = 38% = 0.38=P(E)

Probability of all applicants had a Math SAT score of less than 700 = 100-38=62% = 0.62=P(E')

So, using Bayes theorem, we get that

Probability of admitted applicants had a Math SAT of 700 or more P(E|A)  is given by

$\dfrac{P(E).P(A|E)}{P(E).P(A|E)+P(E').P(A|E')}\\\\=\dfrac{0.38\times 0.34}{0.38\times 0.34+0.62\times 0.16}\\\\=0.57\\\\\approx 57\%$

Hence, our required percentage would be 57%.