Question

There are 30 students in a class and their results are presented as below:

$\begin{array}{ccc}\text{Result}& \text{Pass}& \text{Fail}\\ \text{Number of students}& \text{25}& \text{5}\end{array}$

If a student is taken at random, find the probability that the student has failed the examination.

• A. $\frac{5}{6}$
  
• B. $\frac{1}{6}$
  
• C. $\frac{3}{6}$
  
• D.
  $\frac{25}{60}$
  

Answer 1

The correct option is B $\frac{1}{6}$


Probability of students that failed the examination
$=\frac{\text{Number of students that failed}}{\text{Total number of students}}$

Let the probability of failure as P(F), number of students fail as n(F), and the total sample space as n(s).

$P\left(F\right)=\frac{n\left(F\right)}{n\left(S\right)}P\left(F\right)=\frac{5}{30}=\frac{1}{6}$
So, option b is correct.