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

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

**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 km from her place of work?**

**Answer (i)**

Let E be the event that engineer lives less than 7 km from her place of work.

**P(E) =** (Number of engineers living less than 7 km from their workplaces / Total number of engineers)

**Answer (ii)**

Let F be the event that engineer lives more than or equal to 7 km from her place of work.

**P(F) =** (Number of engineers living more than or equal to 7 km from their workplaces / Total number of engineers)

**Answer (iii)**

Let G be the event that engineer lives within km from her place of work.

**P(G) =** (Number of engineers living within km from their workplaces / Total number of engineers)