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Question

In a certain town25% of families own a phone and15% own a car,65% of families own neither a phone nor a car.2000 families own both a car and a phone. Consider the following statements in this regard

1.10% of families own both a car and a phone

2. 35% of families own either car or a phone

3. 40,000families live in the town?

Which of the above statements are correct?


A

1 and 2

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B

1 and 3

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C

2 and 3

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D

1,2and 3

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Solution

The correct option is C

2 and 3


Explanation for the correct option:

Finding the correct statements:

Let A be the set of people who own phones and B be who own a car, then according to the question,
P(A)=25100,P(B)=15100

Also given,

P(A'B')=65100n(AB)=2000

P(AB)'=65100P(AB)=35100[PA+PA'=1]

Now,

P(AB)=P(A)+P(B)P(AB)

Substituting the values in the above formula we get,

35=25+15n(PC)n(AB)=4035=5n(AB)=5%

But, n(AB)=2000

Total number of families

=[2000×100]5=40000

As, n(AB)=35%

Total number of families=40000

And n(AB)=5%


Hence, the correct option is C.


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