Question

A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 300 responses with the following results:
90 were interested in a interview and documentary, but not reruns
12 were interested in an interview show and reruns, but not a documentary
42 were interested in reruns but not an interview show
72 were interested in an interview show but not a documentary
30 were interested in a documentary and reruns
18 were interested in an interview show and reruns
24 were interested in none of the three

Required:
How many are interested in exactly one kind of show?

Answer 1

Answer:

144

Step-by-step explanation:

The best way to attempt this question is to solve it using a Venn diagram

From the given information, Let;

D = documentaries

I = interview shows

G = game show reruns

From the images attached below, we will see how the Venn diagrams are being drawn step by step and calculated.

i.e

= 300 - (90 + 60 + 24 + 6 + 12 + 18 + 24)

= 300 - 234

= 66

∴

No of those interested in exactly one kind of show = 66 + 60 + 18

= 144

∴$\text{144 are interested in exactly one kind of show.}$