Question

In a group of 100 people, 70 like coffee, 60 like tea, and 45 like both coffee and tea. How many people like neither coffee nor tea?

• A. 5
• B. 10
• C. 15
• D. 20

Answer 1

Answer: (C)

15

Answer 2

n(C) = 70 (number of people who like coffee)

n(T) = 60 (number of people who like tea)

n(C ∩ T) = 45 (number of people who like both coffee and tea)
We need to find n(C' ∩ T'), which represents the number of people who like neither coffee nor tea.

Using the formula:

n(C ∪ T)' = n(U) - n(C ∪ T)

We know:

n(U) = 100

n(C ∪ T) = n(C) + n(T) - n(C ∩ T) = 70 + 60 - 45 = 85

Therefore,
n(C' ∩ T') = 100 - 85 = 15