Question

An organization selected $2400$ families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:

Suppose a family is chosen, find the probability that the family chosen is (i) earning Rs $10000-13000$ per month and owning exactly $2$ vehicles.

(ii) earning Rs $16000$ or more per month and owning exactly $1$ vehicle.

(iii) earning less than Rs $7000$ per month and does not own any vehicle.

(iv) earning Rs $13000-16000$ per month and owning more than $2$ vehicles.

(v) owning not more than $1$ vehicle.

Answer 1

Given, number of total families surveyed $=2400$
Probability of an event $A$ is $P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}$
Where, $n\left(A\right)=$ total number of elements in $A$
$n\left(S\right)=$ total number of elements in sample space(S),
In this case $n\left(S\right)=2400$
(i) Number of families earning Rs $10000­-13000$ per month and owning exactly $2$ vehicles $n\left(A\right)=29$

Hence, required probability is $\therefore P\left(A\right)=\frac{29}{2400}$

(ii) Number of families earning Rs $16000$ or more per month and owning exactly $1$ vehicle $n\left(A\right)=579$

Hence, required probability, $P\left(A\right)=\frac{579}{2400}$
$\therefore P\left(A\right)=\frac{193}{800}$

(iii) Number of families earning less than Rs $7000$ per month and does not own any vehicle $n\left(A\right)=10$

Hence, required probability, $P\left(A\right)=\frac{10}{2400}$
$\therefore P\left(A\right)=\frac{1}{240}$

(iv) Number of families earning Rs $13000­-16000$ per month and owning more than $2$ vehicles $n\left(A\right)=25$

Hence, required probability, $P\left(A\right)=\frac{25}{2400}$
$\therefore P\left(A\right)=\frac{1}{2400}$

(v) Number of families owning not more than $1$ vehicle $n\left(A\right)=10+160+0+305+1+535+2+469+1+579=2062$

Hence, required probability, $P\left(A\right)=\frac{2061}{2400}$
$\therefore P\left(A\right)=\frac{1031}{1200}$