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?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{5}{8}
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?
train