Q. 154.1( 92 Votes )

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:

(i) The number of people who read at least one of the newspapers.

(ii) The number of people who read exactly one newspaper.

Answer :

(i) Let us assume A be the set of people who read newspaper H

Also, let B be the set of people who read newspaper T


And, let C be the set of people who read newspaper I


It is given in the question that,


Number of people who read newspaper H, n (A) = 25


Number of people who read newspaper T, n (B) = 26


Number of people who read the newspaper I, n (C) = 26


Number of people who read both newspaper H and I,


Number of people who read both newspaper H and T,


Number of people who read both newspaper T and I,


And, Number of people who read all three newspaper H, T and I,


Now, we have to find the number of people who read at least one of the newspaper



= 25 + 26 + 26 – 11 – 8 – 9 + 3


= 80 – 28


= 52


There are a total of 52 students who read at least one newspaper.


(ii) Let us assume a be the number of people who read newspapers H and T only


Let b denote the number of people who read newspapers I and H only


Let c denote the number of people who read newspapers T and I only


And, let d denote the number of people who read all three newspapers


It is given in the question that:




Now, we have:




And,


a + d + c +d + b + d = 11 + 8 + 9


a + b + c + d = 28 – 2d


= 28 – 6


= 22


Number of people read exactly one newspaper = 52 – 22


= 30 people

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