Question

100 people who were surveyed and asked the question: ``Is fuchsia kinda pink, or purply?'' Of them, 60 believe that fuchsia is ``kinda pink'' and 27 believe it is both ``kinda pink,'' and also ``purply.'' Another 17 think that fuchsia is neither ``kinda pink'' nor ``purply.''

How many of those 100 people believe that fuchsia is ``purply''?

Answer 1

50

Explanation:

Let the event of people who believe that fuchsia is pink = A

Let the event of people who believe that fuchsia is purply = B

• Since 100 people were surveyed, the Universal Set =100
• 60 believe that fuchsia is ``kinda pink'', n(A)=60
• 27 believe it is both ``kinda pink,'' and also ``purply.'':
  `n(A \cap B) =27`
• 17 think that fuchsia is neither ``kinda pink'' nor ``purply.
  `n(A \cup B)'=17`

We want to determine the number of those who believe that fuchsia is ``purply'', n(B).

In set theory, we have:

`U=n(A)+n(B)-n(A\cap B)+n(A \cup B)'\\100=60+n(B)-27+17\\100=50+n(B)\\n(B)=100-50\\n(B)=50`

Therefore, the number of those who believe that fuchsia is ``purply'' is 50.