An insurance company selected 2000 drivers at random in a particular city to find a relationship between age and accidents. The obtained are given in the following table: Age of Drivers (in years) Accidents in one year 0 1 2 3 over 3 18-29 30-50 above 50 440 505 360 160 125 45 110 60 35 61 22 15 35 18 9 Find the probability of the following events for a driver chosen at random from the life city: being 18-29 years of age and having exactly 3 accidents in one year. being 30-50 years of age and having one or more accidents in a year. having no accidents in one year.

Explanation

Total number of drivers = 2000.
(i) Let `E_(1)` be the number of drivers having ages in 18 - 29 years and exactly 3 accidents in one year
`therefore` `E_(1)=61`
`P(E_(1)) = ("number of drivers of age 18-29 years having exactly 3 accidents in 1 year")/("total number of drivers")`
`= (61)/(2000)`
(ii) Let `E_(2)` be the number of drivers having ages in 30 - 50 years and with one or more accidents in one year
`therefore E_(2) = 125+60+22+18=225`
`P(E_(2)) = ("number of drivers of age 30-50 years with 1 or more accidents in 1 year")/("total number of drivers")`
`=(225)/(2000) = (9)/(80)`
(iii) Let `E_(3)` be the number of drivers having no accidents in one year
`therefore E_(3) = 440+505+360=1305`
`P (E_(3)) = ("number of drivers having no accident in 1 year")/("total number of drivers")`
`=(1305)/(2000) = (261)/(400)`.