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Introduction To Mathematical Modelling

Question
CBSEENMA9003991

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

Vehicles per family

(in र)

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  र 10000–13000 per month and owning exactly 2 vehicles.
(ii) earning र 16000 or more per month and owning exactly l vehicle.
(iii) earning less than र 7000 per month and does not own any vehicle.
(iv) earning र 13000–16000 per month and owning more than 2 vehicles.
(v) owning not more than I vehicle.

Solution

Total number of families selected = 2400
(i) Number of families earning र10000–13000 per month and owning exactly 2 vehicles = 29
∴ Probability that the family chosen is earning र10000–13000 per month and owning
exactly 2 vehicles = 29 over 2400.

(ii) Number of families earning र16000 or more per month and owning exactly 1 vehicle = 579

∴ Probability that the family chosen is earning र16000 or more per month and owning
exactly 1 vehicle = 579 over 2400 equals 193 over 800.

(iii) Number of families earning less than र 7000 per month and does not own any vehicle =10
Probability that the family chosen is earning less than र7000 per month and does not own any vehicle = 10 over 2400 equals 1 over 240
(iv) Number of families earning र13000–16000 per month and owning more than 2 vehicles = 25

∴ Probability that the family chosen is earning र13000–16000 per month and owning
more than 2 vehicles = 25 over 2400 equals 1 over 96.
(v) Number of families owning not more than 1 vehicle

= Number of families owning 0 vehicle + Number of families owning 1 vehicle = (10 + 0+ 1 + 2 + 1) +(160 + 305 + 535 + 469 +579) = 14 + 2048 = 2062
∴ Probability that the family chosen owns not more than 1 vehicle = 2062 over 2400 equals 1031 over 1200