Question

Mrs. Grady surveyed 30 students, 12 of which said they liked basketball, 19 of which said they liked hockey, and 4 of which said they liked both sports.
(a) How many students did not like either sport?(b) How many students liked exactly one of the sports?

Answer 1

Let's do (b) first. You have 2 choices on the survey
1. Basketball
2.Hockey
4 people liked both sports. That means that 4 people circled both. Remove those from your totals. Now, you have 15 pure hockey fans and 8 pure basketball fans.

Add 8 to 15 and you have 23 students who only like one sport.

Now let's do (a).
You have a total of 35 circles on your list. 8 of them are from the 4 "both" people. Remove those.

Now there's 27 circles. Remember how there are 23 students who like one sport? Remove those.

You now have 4 people who didn't circle anything.