Question

In class A of 25 students, 20 passed with \[60\% \] or more marks; in another class B of 30 students, 24 passed with \[60\% \] or more marks. In which class was a greater fraction of students getting with \[60\% \] or more marks?

Answer 1

Hint: First we will first use the formula of the probability of the given event is given by dividing the number of students passed divided by the total number of students, that is; $P = \dfrac{{{\text{Number of students passed}}}}{{{\text{Total number of students}}}}$ to compare the values of class A and B to find required value.

Complete step by step answer:

First, we will consider Class A,
We are given that there are total 25 students.

We are also given that there are 20 students passed with \[60\% \] or more marks.

We know that the probability of the given event is given by dividing the number of students passed divided by the total number of students, that is; $P = \dfrac{{{\text{Number of students passed}}}}{{{\text{Total number of students}}}}$.

Finding the probability of students passed in Class A from the above formula of probability, we get
\[ \Rightarrow P\left( A \right) = \dfrac{{20}}{{25}}\]

Dividing the numerator and denominator of the above equation by 5, we get
\[ \Rightarrow P\left( A \right) = \dfrac{4}{5}\]

We will now consider Class B,
We are given that there are total 24 students.

We are also given that there are 30 students passed with \[60\% \] or more marks.

We know that the probability of the given event is given by dividing the number of students passed divided by the total number of students, that is; $P = \dfrac{{{\text{Number of students passed}}}}{{{\text{Total number of students}}}}$.


Finding the probability of students passed in Class B from the above formula of probability, we get
\[ \Rightarrow P\left( B \right) = \dfrac{{24}}{{30}}\]

Dividing the numerator and denominator of the above equation by 6, we get
\[ \Rightarrow P\left( B \right) = \dfrac{4}{5}\]

Since the probability of both the classes is the same, so same fraction of students got first class in both classes A and B.

Note: In solving these types of questions, you should be familiar with the formula to find the probability of the students passing and not passing. Some students get confused while applying formulae. One can find the probability for one class instead of both classes and then conclude the wrong answer. The total number of students is to be written in the denominator of the probability.