In a random survey 250 people participated. Out of 250 people who took part in the survey, 40 people listen to Pink Floyd. 30 people listen to Metallica and 20 people listen to John Denver. If 10 people listen to all three then find the no. of people who listen only Pink Floyd.

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Solution

The correct option is B

Let the no. of people who listen to Pink Floyd be n(P) = 40
Similarly, the no. of people who listen to Metallica be n(M) = 30
and the no. of people who listen to John Denver be = n(J) = 20
Also given that the no. of people who listen to all three i.e. n(P ∩ M ∩ J) = 10
Let the no. of people who listen only Pink floyd be x.
then, x = (40-30) + (40-20) - 10
Since, (A - (B∩C) = (A - B) ∩ (A - C) (Demorgan's law))
So, x = 20

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In a random survey 250 people participated. Out of 250 people who took part in the survey, 40 people have listened to Pink Floyd. 30 people have listened to metallica and 20 people have listened to John Denver. If 10 people have listened to all three then find the no. of people who have listened only Pink Floyd.

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