# In fall 2014, 38% 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

In fall 2014, 38% 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, 32% 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.)
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Step 1
Let
A - Percent math S A T score of less than 700 or more in all applicants.
B – Percent math SAT score of 700 or more than admitted applicants.
C – Percent math SAT score of less than 700 in admitted applicants.
Step 2
Formula used
$P\left(B\mid A\right)=\frac{P\left(A\mid B\right)P\left(B\right)}{P\left(A\mid C\right)P\left(C\right)+\left(P\left(A\mid B\right)P\left(B\right)\right)}$...(i)
Step 3
Given
$P\left(A\mid B\right)=32\mathrm{%}=0.32$
$P\left(B\right)=38\mathrm{%}=0.38$
$P\left(A\mid C\right)=1-0.32=0.68$
$P\left(C\right)=12\mathrm{%}=0.12$
Step 4
Put these values in(i)
$P\left(A\mid B\right)=\frac{\left(0.32\right)\left(0.38\right)}{\left(0.68\right)\left(0.12\right)\left(\left(0.32\right)\left(0.38\right)\right)}$
$=\frac{0.1216}{0.0816+0.1216}$
$=\frac{0.1216}{0.2032}\approx 0.598425$
Step 5
Percentage of admitted applicants had a Math SAT of 700 or more is $59.84\mathrm{%}\approx 60\mathrm{%}$