A recent survey shows that the ages of 200 workers in a factory is distributed as follows :

If a worker is selected at random , find the probability that the selected worker is
(i) 40 years or more
(ii) under 40 years
(iii) having an age from 30 to 39 years
(iv) under 60 but over 39 years .

Explanation

Total number of workers in the factory = 200 .
(i) Let `E_(1)` be the event of selecting a worker who is 40 years or more . Then ,
P (selecting a worker who is 40 years or more)
= `P(E_(1))`
`= ("number of workers who are 40 years or more")/("total number of workers")`
`= (86 + 46+ 3)/(200) = (135)/(200) = (27)/(40)`.
(ii) Let `E_(2)` be the event of selecting a worker who is under 40 years . Then ,
P(selecting a worker who is under 40 years)
`= P(E_(2))`
`= ("number of workers having an age less than 40 years")/("total number of workers")`
`= (37 + 28)/(200) = (65)/(200) = (13)/(40)`.
(iii) Let `E_(3)` be the event of selecting a worker having an age from 30 to 39 years . Then ,
P(selecting a worker who is under 60 but over 39 years)
`= P(E_(4))`
`= ("number of workers having age more than 39 years but less than 60 years")/("total number of workers")`
`= (86 + 46)/(200) = (132)/(200) = (33)/(50)`.