# The university

At a certain university, 25% of students are in the business faculty. Of the students in the business faculty, 66% are males. However, only 52% of all students at the university are male.

a. What is the probability that a student selected at random in the university is a male in the business faculty?
b. What is the probability that a student selected at random in the university is male or is in the business faculty?
c. What percentage of males are in the business faculty?

Result

a =  16.5 %
b =  74.5 %
c =  66 %

#### Solution:

$a=100 \cdot \ \dfrac{ 25 }{ 100 } \cdot \ \dfrac{ 66 }{ 100 }=\dfrac{ 33 }{ 2 }=16.5=16.5 \%$
$f=1 - 66/100=\dfrac{ 17 }{ 50 }=0.34 \ \\ b=1 - 25/100=\dfrac{ 149 }{ 2 }=74.5 \ \\ \ \\ n=f \cdot \ b=0.34 \cdot \ 74.5=\dfrac{ 51 }{ 200 }=0.255 \ \\ b=100 \cdot \ (1-n)=100 \cdot \ (1-0.255)=\dfrac{ 149 }{ 2 }=74.5=74.5 \%$
$c=66=66 \%$

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