AMC 12 2007a Problem 12

Integers $a, b, c,$ and $d$, not necessarily distinct, are chosen independently and at random from 0 to 2007, inclusive. What is the probability that $ad-bc$ is even?

$\mathrm{(A)}\ \frac 38 \mathrm{(B)}\ \frac 7{16} \mathrm{(C)}\ \frac 12 \mathrm{(D)}\ \frac 9{16} \mathrm{(E)}\ \frac 58$