# Ex.15.1 Q6 Probability Solution - NCERT Maths Class 9

## Question

(i) Find the probability that a student obtained less than \(20\%\) in the mathematics test.

(ii) Find the probability that a student obtained \(60\) marks or above.

## Text Solution

**What is known?**

Marks in different range and respective students.

**What is unknown?**

Probability of students obtained less than \(20\%\) in math. Probability of students obtained \(60\) marks or above.

**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 in range of marks)

\(\begin{align}=\frac{ \begin{pmatrix} \text { Number of students} \\ \text{ in range of marks } \end{pmatrix}}{\text { Total number of students }} \end{align}\)

**Steps:**

Total no of students \(= 90\)

(i)

Probability (a student obtained less than \(20\%\))

\(\begin{align} &= \frac{ \begin{pmatrix} \text{No of students who} \\ \text{ obtained less than $20% $} \end{pmatrix}}{{{\text{Total number of students}}}} \\ &= \frac{7}{90} \end{align}\)

(ii)

Probability (a student obtained \(60\) marks or above)

\(\begin{align} &= \frac{ \begin{pmatrix}\text{No of students obtained } \\ \text{$60$ marks or above} \end{pmatrix}}{{{\text{Total number of students}}}} \\ &= \frac{ (15+8)}{90} =\frac{ 23}{90} \end{align}\)