A rook and a bishop of a standard chess set and having different colors are randomly placed on a standard chessboard.

Determine the probability that one is attacking the other.

This is the same as the probability that a randomly placed queen attacks one of the other 63 squares, randomly chose. For symmetry reasons, you could limit the randomly placed queen to just one quadrant of the board (16 squares). Further, if you weight them appropriately, I think that you only need to place the queen on the four main diagonal squares in the quadrant.

*Edited on ***May 14, 2014, 12:05 pm**