2002 AMC 10P Problem 17

There are 1001 red marbles and 1001 black marbles in a box. Let P_s be the probability that two marbles drawn at random from the box are the same color, and let P_d be the probability that they are different colors. Find |P_s-P_d|.

\text{(A) }0 \qquad \text{(B) }\frac{1}{2002} \qquad \text{(C) }\frac{1}{2001} \qquad \text{(D) }\frac {2}{2001} \qquad \text{(E) }\frac{1}{1000}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.