Red balls and blue balls

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Question from Md., a student:

In a group of 15, 7 have Red Balls, 8 have Blue Balls and 3 have neither.
What fraction of the group has both Red Balls and Blue Balls?

Hi there.

Start crossing off members of the group.

If 3 have neither, that means there are 15-3 = 12 members of the group left.

7 of those members have red balls. That leaves 12-7 = 5 members who have just blue balls.

But you've been told there are 8 members with blue balls, so 8-5 = 3 more members must have blue balls and the only members who could have them already have red balls.

Cheers,
Stephen La Rocque

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.