Answer
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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.
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.
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