Chapter 10 Counting Methods and Probability - 10.4 Finding Probabilities of Disjoint and Overlapping Events - 10.4 Exercises - Skill Practice - Page 710: 26

The student counts the overlap twice because the student forgets to subtract it off.

We know from the equation on page 707 that: $$P(A\ or \ B) = P(A)+P(B)-P(A\ And\ B)$$ Thus, we find: $$=\frac{13}{52}+\frac{12}{52}-\frac{3}{52}=\frac{22}{52}$$