The distance (in km) of 40 engineers from their residence to their place of work were found as follows.

Solution:

(i) Total number of engineers = 40

Number of engineers living less than 7 km from their place of work = 9

Hence, required probability that an engineer lives less than $7 \mathrm{~km}$ from her place of work, $\mathrm{P}=\frac{9}{40}$

(ii) Number of engineers living more than or equal to 7 km from their place of work = 40 − 9 = 31

Hence, required probability that an engineer lives more than or equal to $7 \mathrm{~km}$ from her place of work, $\mathrm{P}=\frac{31}{40}$

(iii) Number of engineers living within $\frac{1}{2} \mathrm{~km}$ from her place of work $=0$

Hence, required probability that an engineer lives within $\frac{1}{2} \mathrm{~km}$ from her place of work, $P=0$