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

## 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 \(0.12 - 0.16\))

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