Question

An insurance company selected 2000 drivers at random in a particular City to find a relationship between rage and accidents data obtained a given in the following table


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

Answer 1

Total number of drivers $=2000$

Number of trials $=2000$

(i) The number of drivers having ages in 18 - 29 years and exactly 3 accidents in one year = 61.

P( driver is 18 - 29 years old with exactly 3 accidents ) $=\frac{61}{2000}$ .

(ii) The number of drivers having ages in 30 - 50 years and with one or more accidents in one year $=125+60+22+18=225$

P( driver is 30 - 50 years old with with one or more accidents in one year ) $=\frac{225}{2000}=\frac{45}{400}=\frac{9}{80}$ .

(iii) The number of drivers having no accidents in one year $=440+505+360=1305$

P( number of drivers having no accidents in one year ) $=\frac{1305}{2000}=\frac{261}{400}.$