# Ex.15.1 Q3 Probability Solution - NCERT Maths Class 9

## Question

Refer to **Example 5**, **Section 14.4**, **Chapter 14.** Find the probability that a student of the class was born in August.

In a particular section of **Class IX**, \(40\) students were asked about the months of their birth and the following graph was prepared for the data so obtained. Find the probability that a student of the class was born in August.

## Text Solution

**What is known?**

Total number of students in class and number of students born in each month.

**What is unknown?**

Probability of students born in the month of August.

**Reasoning:**

The empirical probability \(P(E)\) of an event \(E\) happening, is given by:

\(\begin{align}{P}({E})=\frac{ \begin{bmatrix} \text { Number of trials in which }\\ \text{the event happened } \end{bmatrix} }{ \begin{bmatrix} \text { The total number} \\ \text{of trials } \end{bmatrix} }\end{align}\)

Use probability to derive the solution where

Probability [students born in particular month]

\[\begin{align} & = \frac{\begin{bmatrix}{\text{No of students born }} \\ {\text{in particular month} }\end{bmatrix}}{\begin{bmatrix} \text{Total number of} \\\text{ students in class} \end{bmatrix}} \end{align}\]

**Steps:**

Given total number of students in class \(= 40\)

No of students born in August \(= 6\)

Probability students born in August

\[\begin{align} & { = \frac{\begin{bmatrix} {\text{No of students born in }} \\ {\text{ the }} {\text{month of August}}\end{bmatrix} } { \begin{bmatrix} \text{Total number of}\\ \text{ students in class } \end{bmatrix}} } \\ &= \frac{{\rm{6}}}{{40}} \\&= \frac{3}{{20}}\end{align}\]