Answer
The student adds the overlap instead of subtracting it.
Work Step by Step
We know from the equation on page 707 that:
$$P(A\ or \ B) = P(A)+P(B)-P(A\ And\ B)$$
Thus, we find:
$$=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}=\frac{16}{52}$$