Question

MEDAL GIVEN PLEASE HELP
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 an interview show and a 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.

How many are interested in exactly one kind of show?

Answer 1

@ParthKohli

Answer 2

looks like a direct application of inclusion and exclusion

Answer 3

whats that?

Answer 4

the inclusion-exclusion principle?

the principle says:\[|A \cup B \cup C| = |A|+|B|+|C|-|A \cap B| - |B\cap C| - |A\cap C|+|A\cap B \cap C|\]

Answer 5

this is very clear with a venn diagram

Answer 6

I could use that equation to solve?

Answer 7

Yes you definitely can.

Answer 8

what if I have A B C AND D

Answer 9

Well actually I just read the question again, and it is a little twisted.

Answer 10

can you help me construct it?

Answer 11

The keyword in each of those scenarios is "And"

And usually means more than one, right?

Answer 12

OK, start out with a nice little Venn diagram.

Answer 13

should I draw one on here?