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Question -

A company selected 2400 families at random and survey them to determine a relationship between income level and the number of vehicles in a home. 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
29
82

0
2
1
25
88
If a family is chosen, find the probability that family is:

(i) earning Rs10000-13000 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 vehicle.
(v) owning not more than 1 vehicle
(vi) owning at least one vehicle.



Answer -

The total number of trials is 2400.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by
 
(i) Let A1 be the event that a chosen family earns Rs 10000-13000 per month and owns exactly 2 vehicles.
The number of times A1 happens is 29.
Therefore, we have 
(ii) Let A2 be the event that a chosen family earns Rs 16000 or more per month and owns exactly 1 vehicle.
The number of times A2 happens is 579.
Therefore, we have 
(iii) Let A3 be the event that a chosen family earns less than Rs 7000 per month and does not owns any vehicles.
The number of times A3 happens is 10.
Therefore, we have
(iv) Let A4 be the event that a chosen family earns Rs 13000-16000 per month and owns more than 2 vehicles.
The number of times A4 happens is 25.
Therefore, we have
 
(v) Let A5 be the event that a chosen family owns not more than 1 vehicle (may be 0 or 1). In this case the number of vehicles is independent of the income of the family.
The number of times A5 happens is
 .
Therefore, we have
(vi) Let A6 be the event that a chosen family owns atleast 1 vehicle (may be 1 or 2 or above 2). In this case the number of vehicles is independent of the income of the family.
The number of times A6 happens is
 .
Therefore, we have

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