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.

 Video Solution
Probability
Ex exercise-15-1 | Question 10

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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