# Ex.15.1 Q7 Probability Solution - NCERT Maths Class 9

## Question

To know the opinion of the students about the subject statistics, a survey of \(200\) students was conducted. The data is recorded in the following table.

Find the probability that a student chosen at random

(i) likes statistics,

(ii) does not like it.

## Text Solution

**What is known?**

Number of students who like statistics and who do not like statistics.

**What is the unknown?**

Probability of number of students who like statistics and who do not like statistics.

**Reasoning:**

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

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

Use probability to derive the solution where

Probability (students like/dislike statistics)

\(\begin{align}=\frac{ \begin{pmatrix} \text { Number of students who } \\ \text{like or dislike statistics } \end{pmatrix} }{\text { Total number of students }}\end{align}\)

**Steps:**

Total no of students \(= 200\)

(i) Likes statistics

Probability students like statistics

\[\begin{align}&\text{ = }\frac{\text{No of students like statistics }}{\text{ Total no of students}} \\ & \text{= }\frac{135}{200}\text{=}\frac{27}{40} \end{align}\]

(ii) Does not likes statistics

Probability students dislike statistics

\[\begin{align}&\text{ = }\frac{\text{No of students dislike statistics }}{\text{ Total no of students}} \\ & \text{= }\frac{65}{200}\text{=}\frac{13}{40} \end{align}\]