22% committed crimes, 28% attended college, and 56% did neither.

Question

What percent of people in the study both committed a crime and attended college?

Answer 1

Using probability notation, you know 3 things:

 

1. P (crime) = .22

2. p (college) = .28

3. P (not crime and not college) = .56

 

But the third P is the same as:  P (not (crime OR college)).  That means that P (crime or college) = 1 - .56 = .44.

 

However, we also know that P (crime or college) = P (crime) + P (college) - P (crime AND college).

 

So .44 = .22 + .28 - P (crime AND college) = .50 - P (crime AND college)

 

So P (crime AND college) must equal .06, or 6%.  That's what the problem asked us to solve, so that's the answer.