# Ex.15.1 Q10 Probability Solution - NCERT Maths Class 9

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## Question

A study was conducted to find out the concentration of sulphur dioxide in the air parts per million ($$\rm ppm$$) of a certain city. The data obtained for $$30\,\rm days$$ is as follows.

 $$0.03$$ $$0.08$$ $$0.08$$ $$0.09$$ $$0.04$$ $$0.17$$ $$0.16$$ $$0.05$$ $$0.02$$ $$0.06$$ $$0.18$$ $$0.2$$ $$0.11$$ $$0.08$$ $$0.12$$ $$0.13$$ $$0.22$$ $$0.07$$ $$0.08$$ $$0.01$$ $$0.1$$ $$0.06$$ $$0.09$$ $$0.18$$ $$0.11$$ $$0.07$$ $$0.05$$ $$0.07$$ $$0.01$$ $$0.04$$

find the probability of the concentration of sulphur dioxide in the interval $$0.12 - 0.16$$ on any of these days.

## Text Solution

What is known

Concentration of sulphur dioxide for $$30$$ days.

What is unknown?

Probability of the concentration of sulphur dioxide in the interval $$0.12 - 0.16.$$

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 (Concentration of Sulphur dioxide )

\begin{align}=\frac{ \begin{pmatrix} \text { Number of days of} \\ \text{ specific concentration } \end{pmatrix} }{\text { Total number of days }} \end{align}

Steps:

Total no of days $$= 30$$

No of days on which concentration was in the interval $$0.12-0.16 = 2$$

Probability (Concentration of Sulphur dioxide in the interval $$0.12 - 0.16$$)

\begin{align}\\&=\frac{ \begin{pmatrix} \text { Number of days when } \\ \text{ concentration was in} \\ \text{ the interval } 0.12-0.16 \end{pmatrix} }{\text { Total number of days }} \\ &=\frac{2}{30}=\frac{1}{15}\end{align}

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