Question

In a school 25 students passed out of 30 in section A and 24 students passed out of 40 in section B. Which section is shown better results?

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 the required value.

Complete step by step answer:
First, we will consider section A,
We are given that there are a total of 30 students.
We are also given that there are 25 students who passed.
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 section A from the above formula of probability, we get
$ \Rightarrow P\left( A \right) = \dfrac{{25}}{{30}}$
Divide numerator by denominator,
$ \Rightarrow P\left( A \right) = 0.83$
Now, we will consider section B,
We are given that there are a total of 40 students.
We are also given that there are 24 students passed.
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 section B from the above formula of probability, we get
$ \Rightarrow P\left( B \right) = \dfrac{{24}}{{40}}$
Divide numerator by denominator,
$ \Rightarrow P\left( B \right) = 0.6$
Since the probability of section A is more than section B.

Hence, section A has shown better results.

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.