What is the empirical probability that an engineer lives: (i) less than 7 km from her place of work? (ii) more than or equal to 7 km from her place of work? (iii) within 12 km from her place of work?The distance (in km) of 40 engineers from their residence to their place of work were found as follows:

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What is the empirical probability that an engineer lives:
(i) less than 7 km from her place of work?
(ii) more than or equal to 7 km from her place of work?
(iii) within $\frac{1}{2}$ km from her place of work?
The distance (in km) of 40 engineers from their residence to their place of work were found as follows:

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Detailed Solution

(i)

Distance (in km)	No. of engineers
Less than 7 km	9
More than or equal to 7 km	31
Total	40

Let $A$ be the event of engineers living less than 7km from their place of work

Total number of engineers $n (S) = 40 .$
Number of engineers living less than 7km from their place of work $n (A) = 9 .$
Thus, the required probability $p (A) = \frac{n (A)}{n (S)} = \frac{9}{40} .$

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