Question

There are $100$ students in a class. $24$ of the students in the class have brown hair. If a student is called up at random, what is the probability that the student possess brown hair?

• A. $\frac{6}{25}$
  
• B. $\frac{1}{24}$
  
• C. $\frac{1}{100}$
  
• D. $\frac{24}{25}$
  

Answer 1

The correct option is A $\frac{6}{25}$


Given:
$\bullet$ Total students in the class $=100$
$\bullet$ Number of students with brown hair in the class $=24$

Selection of a student that possess brown hair can be done in ${}^{24}{C}_1$ ways.
Selection of a student from the class can be done in ${}^{100}{C}_1$ ways.

Let $\text{P(Brown)}$ denotes the probability that the student selected at random possess brown hair.

Number of favorable outcomes $=$
Selection of a student that possess brown hair $={}^{24}{C}_1$
Total number of outcomes $=$ Selection of a student from the class $={}^{100}{C}_1$

$\text{P(Brown)}=\frac{\text{Selection of a student that possess brown hair}}{\text{Selection of a student from the class}}$
$\text{P(Brown)}=\frac{{}^{24}{C}_1}{{}^{100}{C}_1}$
$\text{P(Brown)}=\frac{24}{100}$

$(\because {}^n{C}_1=\frac{n!}{1!(n-1)!}=n)$

$\text{P(Brown)}=\frac{6}{25}$

Therefore, option (a.) is the correct answer.