An insurance company selected $2000$ drivers at random (i.e., without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained is given in the following table:
Find the probabilities of the following events for a driver chosen at random from the city:
(i) The driver being in the age group $18 - 29$ years and having exactly $3$ accidents in one year.
(ii) The driver being in the age group of $30 - 50$ year and having one or more accidents in a year.
(iii.) Having no accidents in the year.

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Solution

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 $= 61.$
Probability ( 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 $= 125 + 60 + 22 + 18 = 225$
Probability ( driver is 30 - 50 years old with with one or more accidents in one year ) = $\frac{225}{2000} = \frac{9}{80}$ .
(iii) The number of drivers having no accidents in one year $= 440 + 505 + 360 = 1305$
Probability ( number of drivers having no accidents in one year) = $\frac{1305}{2000} = \frac{261}{400}$ .

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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.