# 3 Circle Venn Diagram Probabilities

For exam revision, I was looking over some exam problems and I'm stuck on this current problem.

The question is to draw up a Venn Diagram based on the information given below.

60 adults were surveyed about their movie preferences. 38 liked horror movies, 42 liked comedy movies and 35 liked thrillers. 13 liked all three genres. 25 liked horror and thrillers and 4 only liked horrors. None of the adults liked none of those three genres.

I have filled what is given but I am unsure of what to do next.

• Hi, welcome to the site. Could you please specify what the question is? If this is homework, a "self study" tag is appropriate. – Easymode44 Aug 29 '18 at 7:53

You can do the following:

• let x denotes the adults who only liked comedy movies.
• y denotes the adults who liked comedy and Thriller movies and
• z denotes the adults who only liked Thriller movies.

So, from your Venn Diagram, following are the equations,

Total number of adults who liked Comedy movies
9 + 13 + x + y = 42 ==>   x + y = 20

Total number of adults who liked Thriller movies
13 + 12 + y + z = 35 ==>   y + z = 10

Total number of adults who liked either only Comedy or only Thriller  or (Comedy and Thriller)
x + y + z = 60 - (13 + 12 + 9 + 4)  ==>  x + y + z = 22


Solving these equation would give,

x = 12, y = 8 and z = 2