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:
Monthly income (in Rs.) / Vehicles per family $0$ $1$ $2$ Above $2$ Less than $7000$ $10$ $160$ $25$ $0$ $7000 - 10000$ $0$ $305$ $27$ $2$ $10000 - 13000$ $1$ $535$ $29$ $1$ $13000 - 16000$ $2$ $469$ $59$ $25$ $16000$ or more $1$ $579$ $82$ $88$
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.
| Monthly income (in Rs.) / Vehicles per family | $0$ | $1$ | $2$ | Above $2$ |
| Less than $7000$ | $10$ | $160$ | $25$ | $0$ |
| $7000 - 10000$ | $0$ | $305$ | $27$ | $2$ |
| $10000 - 13000$ | $1$ | $535$ | $29$ | $1$ |
| $13000 - 16000$ | $2$ | $469$ | $59$ | $25$ |
| $16000$ or more | $1$ | $579$ | $82$ | $88$ |
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.
(N/A) Total number of families surveyed $= 2400$.
$(i)$ Number of families earning Rs. $10000 - 13000$ per month and owning exactly $2$ vehicles $= 29$.
Probability $= \frac{29}{2400}$.
$(ii)$ Number of families earning Rs. $16000$ or more per month and owning exactly $1$ vehicle $= 579$.
Probability $= \frac{579}{2400}$.
$(iii)$ Number of families earning less than Rs. $7000$ per month and owning no vehicle $= 10$.
Probability $= \frac{10}{2400} = \frac{1}{240}$.
$(iv)$ Number of families earning Rs. $13000 - 16000$ per month and owning more than $2$ vehicles $= 25$.
Probability $= \frac{25}{2400} = \frac{1}{96}$.
$(v)$ Number of families owning not more than $1$ vehicle (i.e.,$0$ or $1$ vehicle) $= (10 + 160) + (0 + 305) + (1 + 535) + (2 + 469) + (1 + 579) = 170 + 305 + 536 + 471 + 580 = 2062$.
Probability $= \frac{2062}{2400} = \frac{1031}{1200}$.
$(i)$ Number of families earning Rs. $10000 - 13000$ per month and owning exactly $2$ vehicles $= 29$.
Probability $= \frac{29}{2400}$.
$(ii)$ Number of families earning Rs. $16000$ or more per month and owning exactly $1$ vehicle $= 579$.
Probability $= \frac{579}{2400}$.
$(iii)$ Number of families earning less than Rs. $7000$ per month and owning no vehicle $= 10$.
Probability $= \frac{10}{2400} = \frac{1}{240}$.
$(iv)$ Number of families earning Rs. $13000 - 16000$ per month and owning more than $2$ vehicles $= 25$.
Probability $= \frac{25}{2400} = \frac{1}{96}$.
$(v)$ Number of families owning not more than $1$ vehicle (i.e.,$0$ or $1$ vehicle) $= (10 + 160) + (0 + 305) + (1 + 535) + (2 + 469) + (1 + 579) = 170 + 305 + 536 + 471 + 580 = 2062$.
Probability $= \frac{2062}{2400} = \frac{1031}{1200}$.
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