An insurance company selected `2000` drivers at random in particular city to find a relationship between age and accidents . The data obtained are given in the following table .

Find the probability of each of the following events for a driver chosen at random from the city :
`(i)` being `18-29` years of age and having exactly `3` accidents in one year .
`(ii)` being `30-50` years of age and having one or more accidents in one year
`(iii)` having no accident in one year .

Explanation

Total number of drivers = 2000.
(i) Let `E_(1)` be the event of choosing drivers of age 18-29 years with exactly 3 accidents in a year . Then ,
P(choosing drivers of age 18-29 years with exactly 3 accidents in a year . Then ,
P(choosing drivers of age 18-29 years with exactly 3 accidents in one year )
=`P(E_(1))`
`= ("number of drivers of age 18-29 years having exactly 3 accidents in 1 year")/("total number of drivers")`
`= (60)/(2000) = (3)/(100)` .
(ii) Let `E_(2)` be the event of choosing drivers of age 30-50 years and having one or more accidents in one year . Then ,
P(choosing drivers of age 30-50 years with 1 or more accidents in 1 year)
`= P(E_(2))`
= `("number of drivers of age 30-50 years with 1 or more accidents in 1 year")/("total number of drivers")`
`= (125 + 60 + 22 + 18)/(2000) = (225)/(2000) = (9)/(80)`.
(iii) Let `E_(3)` be the event of choosing drivers having no accident in 1 year . then ,
P(choosing drivers having no accident in 1 year)
= `P (E_(3))`
`= ("number of drivers having no accident in 1 year")/("total number of drivers")`
`= (440 + 505 + 360)/(2000) = (1305)/(2000) = (261)/(400)`.