Question

An insurance company selected $1600$ drivers in a particular city to find the relationship between age and number of accidents. The data obtained are given in the following table. Find the probabilities of the following events for a driver chosen at random from the city.
(i) being $25-40$ years of age and having more than $2$ accidents in one year.
(ii) being above $40$ years of age and having accidents more than 1 but less than $3$ in one year.
(iii) having no accidents in one year.
(iv) being below $25$ years of age and having at most $2$ accidents in one year.

Answer 1

$Totaldrivers=1600$

$i)P$(being $25-40$ years of age

having more than $2$ accidents) $=\frac{No.offavourableoutcome}{Totalno.ofoutcomes}$

$=\frac{15+10}{1600}=\frac{25}{1600}$

$=0.015$

$ii)P$ (being $40$ years above and having

accidents more than $1$ and less than $3$) $=\frac{13+17}{1600}$

$=\frac{30}{1600}=0.018$

$iii)P$(having no accidents) $=\frac{320+400+150+150}{1600}$

$=\frac{1020}{1600}=0.063$

$iv)P$(below $25$ years and having atmost $2$ accident ) $=\frac{320+125+75}{1600}$

$=\frac{515}{1600}$

$=0.032$