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 the university's men are in the business faculty?

Correct answer:

a =  16.5 %
b =  74.5 %
c =  66 %

Step-by-step explanation:

$a=100\cdot \frac{25}{100}\cdot \frac{66}{100}=\frac{33}{2}\%=16.5\%$

$$\begin{gathered} f=1-66/100=\frac{17}{50}=0.34 \\ b=1-25/100=\frac{149}{2}=74.5 \\ n=f\cdot b=\frac{17}{50}\cdot \frac{149}{2}=\frac{17\cdot 149}{50\cdot 2}=\frac{2533}{100}=\frac{51}{200}=0.255 \\ b=100\cdot (1-n)=100\cdot (1-\frac{51}{200})=\frac{149}{2}\%=74.5\% \end{gathered}$$

$c=66=66\%$

Try another example