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?

Correct result:

a =  16.5 %
b =  74.5 %
c =  66 %

Solution:

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

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

$c=66=66\mathrm{\%}$

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Showing 1 comment:

Math student

Question C) seems a bit misleading as one might think that it requires the percentage that male business students make up of the whole male population of students at the university.

6 months ago  Like

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