Question

22. In a survey of 26 instructors, it was found that 11 liked whiteboards, 18 like blackboards, and 8 liked both. How many instructors like whiteboards only? How many instructors liked blackboards only? How many instructors liked neither?

Answer 1

a) 3

b) 10

c) 5

Explanation:

We are given the following in the question:

Sample size, n = 26

Instructor that like whiteboards = 11

`n(A) = 11`

Instructor that like blackboards = 18

`n(B) = 18`

Instructor that like both boards = 8

`n(A\cap B) = 8`

We have to find the following:

a) instructors like whiteboards only

`=n(A) - n(A\cap B)\\=11-8\\=3`

b) instructors liked blackboards only

`=n(B) - n(A\cap B)\\=18-8\\=10`

c) instructors liked neither

`=n(A\cup B)'\\=n - n(A\cup B)\\=n - (n(A) + n(B) -n(A\cap B))\\=26-(11+18-8)\\=5`