27 Aug 06
2 edits
Originally posted by ThudanBlunderIsn't it the probability that two queens attack each other? That can't be too hard to figure out...
If a rook and a bishop are placed on two randomly chosen squares of the board, what is the probability that either one of them will attack the other?
...Edit: if you count placing them on the same square as "attacking each other" then it's
(64 + 64*14 + B)/(64*64)
where the B is the total number of squares a bishop can attack by placing it on all 64 squares of the chessboard. Starting from the middle four squares in the centre, and working outwards in concentric squares, we see
B = 4*13 + 12*11 + 20*9 +28*7 = 560
so the probability is 95/256. If you're not counting them being on the same square then take off the first 64 above to yield 91/256.