In a survey of 60 people, it was found that 25 people read newspaper H

1.	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: the number of people who read exactly one newspaper.
Answer» Let A be the set of people who read newspaper H. Let B be the set of people who read newspaper T. Let C be the set of people who read newspaper I. Given n(A) = 25, n(B) = 26, and n(C) = 26 n(A∩C) = 9, n(A∩B) = 11, and (B∩C) = 8 n(A∩B∩C) = 3 Let U be the set of people who took part in the survey. n(A∪B∪C) = n(A) + n(B) + n(C) − n(A∩B) − n(B∩C) − n(C∩A) + n(A∩B∩C) = 25 + 26 + 26 − 11 − 8 − 9 + 3 = 52 Hence, 52 people read at least one of the newspaper.

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: the number of people who read exactly one newspaper.

Answer»

Let A be the set of people who read newspaper H.

Let B be the set of people who read newspaper T.

Let C be the set of people who read newspaper I.

Given n(A) = 25, n(B) = 26, and n(C) = 26

n(A∩C) = 9, n(A∩B) = 11, and (B∩C) = 8

n(A∩B∩C) = 3

Let U be the set of people who took part in the survey.

n(A∪B∪C) = n(A) + n(B) + n(C) − n(A∩B) − n(B∩C) − n(C∩A) + n(A∩B∩C)

= 25 + 26 + 26 − 11 − 8 − 9 + 3

= 52

Hence, 52 people read at least one of the newspaper.