An organisation selected 2400 families at random and surveyed them to determine a relationship

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

7000 – 10000

10000 – 13000

13000 – 16000

16000 or more

10

0

1

2

1

160

305

535

469

579

25

27

29

59

82

0

2

1

25

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

Report

Question

Total number of families = 2400

(i) Number of families earning Rs. 10,000 – 13,000 per month and owning exactly two vehicles = 29

Hence,

Probability of families earning Rs. 10,000 – 13,000 per month and owning exactly two vehicles will be,

= No. of families earning Rs. 10000-13000 per month and owning exactly two vehicles/Total number of families

= 29/2400

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

Hence,

Probability of families earning Rs. 16000 or more per month and owning exactly one vehicle will be,

= No. of families earning Rs. 16000 or per month and owning exactly one vehicles/Total number of families

= 579/2400

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

Hence,

Probability of families earning less than Rs. 7,000 per month and doesn’t own any vehicles will be,

= No. of families earning Rs. 7000 per month and owning exactly no vehicles/Total number of families

= 10/2400

= 1/240

(iv) Number of families earning Rs. 13,000-16000 per month and owning more than two vehicles = 25

Hence,

Probability of families earning Rs. 13,000-16000 per month and owning more than two vehicles will be,

= No. of families earning Rs. 7000 per month and owning exactly no vehicles/Total number of families

= 25/2400

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

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

= 2062

Hence,

Probability of families owning not more than one vehicle will be

= No. of families owning exactly not more than one vehicles/Total number of families

= 2062/2400

= 1031/1200

solved 5

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