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
[tex]\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\%[/tex]
Hence, our required percentage would be 57%.
