 Questions & Answers    Question Answers

# The distance $({\text{in }}km)$ of $40$ engineers from their residence to their workplace were found as follows:$\begin{array}{*{20}{c}} 5&3&{10}&{20}&{25}&{11}&{13}&7&{12}&{31} \\ {19}&{10}&{12}&{17}&{18}&{11}&{32}&{17}&{16}&2 \\ 7&9&7&8&3&5&{12}&{15}&{18}&3 \\ {12}&{14}&2&9&6&{15}&{15}&7&6&{12} \end{array}$What is the empirical probability that an engineer lives:i) Less than $7{\text{ }}km$ from her place of work?ii) More than or equal to $7{\text{ }}km$ from her place of work?iii) Within $\dfrac{1}{2}{\text{ }}km$ from her place of work?  Answer Verified
Hint: Here empirical probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trails, not in a theoretical sample space but in an actual experiment.

Complete step-by-step answer:
Given that total number of engineers $= 40$
From the above data it is clear that,
Number of engineers who live at a distance of less than $7{\text{ }}km$ from their place of work $= 9$
Number of engineers who live at a distance which is more than or equal to $7{\text{ }}km$ from their place of work $= 40 - 9 = 31$
Number of engineers living within $\dfrac{1}{2}{\text{ }}km$ from their place of work $= 0$
$P({\text{engineer lives less than }}7km{\text{ from her place of work) = }}\dfrac{{{\text{number of engineers living less than }}7km{\text{ from their place of work}}}}{{{\text{total number of engineers}}}} \\ {\text{ = }}\dfrac{9}{{40}} \\$

$P({\text{engineer lives more than or equal }}7km{\text{ from her place of work) = }}\dfrac{{{\text{number of engineers living more than or equal to }}7km{\text{ from their place of work}}}}{{{\text{total number of engineers}}}} \\ {\text{ = }}\dfrac{{31}}{{40}} \\$

$P({\text{engineer lives less than }}\dfrac{1}{2}km{\text{ from her place of work) = }}\dfrac{{{\text{number of engineers living less than to }}\dfrac{1}{2}km{\text{ from their place of work}}}}{{{\text{total number of engineers}}}} \\ {\text{ = }}\dfrac{0}{{40}} \\ \\ {\text{ = 0}} \\$

Hence the empirical probability that an engineer lives
i) Less than $7{\text{ }}km$ from her place of work $= \dfrac{9}{{40}}$
ii) More than or equal to $7{\text{ }}km$ from her place of work $= \dfrac{{31}}{{40}}$
iii) Within $\dfrac{1}{2}{\text{ }}km$ from her place of work $= 0$

Note: The probability of an event $E$ always obeys the condition $0 \leqslant P(E) \leqslant 1$. And also, the total number of outcomes in an event is always less than the total number of outcomes is the sample space.
Bookmark added to your notes.
View Notes
Perpendicular Distance Of A Point From A Plane  Factors of 40  Table of 40 - Multiplication Table of 40  Probability For Class 10  Log Values From 1 to 10  Height and Distance  CBSE Class 10 Maths Chapter 15 - Probability Formula  Three Dimensional Shapes  Distance Between Two Points  Types of Events in Probability  