Question

A survey was conducted to determine the popularity of three foods among students. The data collected from 75 students are summarized above. What is the number of students who like none or only one of the foods?

Answer 1

20

Explanation:

Total no = 75

N (P) = 48 , N (H) = 45 , N (T) = 58

N (P∩H) = 28 , N (H∩T) = 37 , N (P∩T) = 40

N (P∩H∩T) = 25

Total no = N (P) + N (H) + N (T) - N (P∩H) - N (H∩T) - N (P∩T) + N (P∩H∩T) + neither

75 = 48 + 45 + 58 - 28 - 37 - 40 + 25 + neither

75 = 71 + neither → neither = 4

N (only P) = N (P) - N (P∩H) - N (P∩T) + N (P∩H∩T) = 48 - 28 - 40 + 25 = 5

N (only H) = N (H) - N (P∩H) - N (H∩T) + N (P∩H∩T) = 45 - 28 - 37 + 25 = 5

N (only T) = N (T) - N (H∩T) - N (P∩T) + N (P∩H∩T) = 58 - 37 - 40 + 25 = 6

So, total liking either one or neither = 4 + 5 + 5 + 6 = 20