Question

A survey of the readers of three daily news papers; Nation, standard and Kenya times showed the following results. i) A total of 100 million people read Nation ii) A total of 55 people read Kenya times iii) A total of 50 people read standard. iv) 30 people read both Nation and Kenya times v) 20 people read both Nation and standard. vi) 15people read both standard and Kenya times vii) The total number of people interviewed for which papers they read was 250 million. viii) 10 read all the daily newspaper. Required Calculate the number of people who do not read any of this newspaper.

Answer 1

N(N ∩ S ∩ K) = 10
n(ξ) = 250
n(S ∪ K) = 15 - 10 = 5
n(N ∪ S) = 20 - 10 = 10
n(N ∪ K) = 30 - 10 = 20
n(S) = 50 - 10 - 5 - 10 = 25
n(K) = 55 - 20 - 5 - 10 = 20
n(N) = 100 - 10 - 20 - 10 = 60

n(N ∪ S ∪ K) = 10 + 5 + 10 + 20 + 25 + 20 + 60 = 150

Therefore, n(N ∪ S ∪ K)' = 250 - 150 = 100

Therefore, 100 million people do not read any of the three papers.