Question

Vehicles per family $\Rightarrow$ Monthly income (Rs.) $\Downarrow$	0	1	2	Above 2
Less than 7,000	10	160	25	0
7,000 - 10,000	0	305	27	2
10,000 - 13,000	1	535	29	1
13,000 - 16,000	2	469	59	25
16,000 or more	1	579	82	88

An organisation 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

Number of families surveyed

$=10+60+25+0+0+305+27+2+1+535+29+1+2+469+55+25+579+82+88$

$=2400$

(i) Number of families earning Rs. $10000-13000$ per month and owning exactly $2$ vehicles $=29$

$P=\frac{29}{2400}$

(ii) Number of families earning Rs. 16000 or more per month and owning exactly $1$ vehicle $=579$

$P=\frac{579}{2400}$

(iii) Number of families earning less than Rs. $7000$ per month and does not own any vehicle $=10$

$P=\frac{10}{2400}=\frac{1}{240}$

(iv) Number of families earning Rs. $13000-16000$ per month and owning more than $2$ vehicles $=25$
$P=\frac{25}{2400}=\frac{1}{96}$

(v) Number of families owning not more than $1$ vehicle

$=10+160+0+305+1+535+2+469+1+579=2062$

$P=\frac{2062}{2400}=\frac{1031}{1200}$