Question 12Integers $a,$ $b,$ $c,$ 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?$\dfrac{3}{8}$$\dfrac{7}{16}$$\dfrac{1}{2}$$\dfrac{9}{16}$$\dfrac{5}{8}$