Two boxes, $X$ and $Y$, contain red, blue, and green pens. Box $X$ contains 2 red pens, 5 blue pens, and 3 green pens. Box $Y$ contains 6 red pens, 2 blue pens, and 2 green pens. Casey picks one pen at random from Box $X$ and places it into Box $Y$. Casey then picks one pen at random from Box $Y$.