# Ex.15.1 Q9 Probability Solution - NCERT Maths Class 9

## Question

Eleven bags of wheat flour, each marked \(5\,\rm kg\), actually contained the following weights of flour (in kg)

\(4.97, 5.05, 5.08, 5.03,\\ 5.00, 5.06, 5.08,\\ 4.98, 5.04, 5.07, 5.00\)

Find the probability that any of these bags chosen at random contains more than \(5 \,\rm kg\) of flour.

## Text Solution

**What is known?**

No of bags of specific weights.

**What is unknown?**

Probability of any of the bags containing more than \(5\,\rm kg\) of flour.

**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 \(P\) Weight of the bag

\(\begin{align}=\frac{ \begin{pmatrix} \text { Number of bags} \\ \text{ of specific weight } \end{pmatrix} }{\text { Total number of bags }}\end{align}\)

**Steps:**

Total no of bags \(= 11\)

No of bags more than \(5\,\rm kg\) of flour \(= 7\)

Probability (Bag weighing more than \(5\,\rm kg\) of flour )

\(\begin{align}\\&=\frac{ \begin{pmatrix} \text { Number of bags weighing} \\ \text{ more than $5$ kg of flour } \end{pmatrix}} {\text { Total number of bags }} \\ &=\frac{7}{11}\end{align}\)