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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."
Given:
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.
A family is chosen.
To do:
We have to 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.
Solution:
(i) Total number of families $=2400$
Number of families earning Rs 10000-13000 per month and owning exactly 2 vehicles $=29$
We know that,
Probability of an event=$ \frac{Number \ of \ favourable \ outcomes}{Total \ number \ of \ outcomes}$
Therefore,
Probability that the family is earning Rs 10000-13000 per month and owning exactly 2 vehicles $=\frac{29}{2400}$
The probability the family is earning Rs 10000-13000 per month and owning exactly 2 vehicles is $\frac{29}{2400}$.
(ii) Total number of families $=2400$
Number of families earning Rs 16000 or more per month and owning exactly 1 vehicle $=579$
We know that,
Probability of an event=$ \frac{Number \ of \ favourable \ outcomes}{Total \ number \ of \ outcomes}$
Therefore,
Probability that the family is earning Rs 16000 or more per month and owning exactly 1 vehicle $=\frac{579}{2400}$
The probability the family is earning Rs 16000 or more per month and owning exactly 1 vehicle is $\frac{579}{2400}$.
(iii) Total number of families $=2400$
Number of families earning less than Rs 7000 per month and does not own any vehicle $=10$
We know that,
Probability of an event=$ \frac{Number \ of \ favourable \ outcomes}{Total \ number \ of \ outcomes}$
Therefore,
Probability that the family is earning less than Rs 7000 per month and does not own any vehicle $=\frac{10}{2400}$
$=\frac{1}{240}$
The probability the family is earning less than Rs 7000 per month and does not own any vehicle is $\frac{1}{240}$.
(iv) Total number of families $=2400$
Number of families earning Rs 13000-16000 per month and owning more than 2 vehicles $=25$
We know that,
Probability of an event=$ \frac{Number \ of \ favourable \ outcomes}{Total \ number \ of \ outcomes}$
Therefore,
Probability that the family is earning Rs 13000-16000 per month and owning more than 2 vehicles $=\frac{25}{2400}$
$=\frac{1}{96}$
The probability the family is earning Rs 13000-16000 per month and owning more than 2 vehicles is $\frac{1}{96}$.
(v) Total number of families $=2400$
Number of families owning not more than 1 vehicle $=10 + 0 + 1 + 2 + 1 + 160 + 305 + 535 + 469 + 579=2062$
We know that,
Probability of an event=$ \frac{Number \ of \ favourable \ outcomes}{Total \ number \ of \ outcomes}$
Therefore,
Probability that the family is owning not more than 1 vehicle $=\frac{2062}{2400}$
$=\frac{1031}{1200}$
The probability the family is owning not more than 1 vehicle is $\frac{1031}{1200}$.
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