Question

The grade marks of 50 students of a class are recorded as below

A student of the class is selected at random, what is the probability that the selected student has obtained grade A?
$$\begin{gathered} \text{A}\text{. }{\displaystyle \frac{4}{25}} \\ \text{B}\text{. }{\displaystyle \frac{16}{50}} \\ \text{C}\text{. }{\displaystyle \frac{4}{50}} \\ \text{D}\text{. }{\displaystyle \frac{8}{25}} \end{gathered}$$

Answer 1

Hint: Here, we will be using the general formula for the probability of occurrence of an event, i.e., $P(A)={\displaystyle \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}}$

Complete step by step answer:

Given, Total number of students in a class$=50$

According to the given data in the table, we can say that

Number of students having grade C$=13$, 

Number of students having grade B$=17$, 

Number of students having grade A$=8$ 

And, Number of students having grade A+$=12$

As we know that the general formula for probability is given by

Probability of occurrence of an event $={\displaystyle \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}}$

Here, the favorable event is that the selected student has obtained grade A.

So, Number of favorable outcomes $=$ Number of students who has obtained grade A$=8$

Total number of possible outcomes $=$ Total number of students in a class$=50$

Therefore, Required probability $={\displaystyle \frac{8}{50}}={\displaystyle \frac{4}{25}}$

Hence, the probability that the selected student has obtained grade A is ${\displaystyle \frac{4}{25}}$. So, Option (A) is correct.

Note: In these types of problems, the favorable event is the event whose probability is asked to find out. In this particular problem, extra data is also provided in the question itself (number of students who have obtained grades C, B and A+) which is not being used anywhere to get to the answer.