Not sure how to work this one

Question

27 students;

20 like video games;

16 like comic books;

12 like video games and comic books;

 

how many like neither?

Answer 1

This is easiest to see if we construct the probability space.

 

Let's define several variables.

 

The event C is the probability that a student likes comic books and the event C- is the probability that a student does not like comic books.

 

The event V is the probability that a student likes video games and the event V- is the probability that a student does not like video games.

 

Since there are 27 students total and 20 like video games while 16 like comic books and 12 like both.

 

That means if 12 like both, then those that like video games and don't like comic books is 4 (or 16 total less the 12 that liked both) and since 20 liked video games and 12 liked both, then 8 liked video games but did not like comics. 

 

Since 12 liked both and 8 liked video but not comics and 4 likes comics but not video, that leaves 3 (27 total less 12 less 8 less 4) that did not like comics and did not like video games.

 

How many like neither? 3