If two cells are chosen randomly on a 8x8 chessboard what is the probability that they are neighbors (i.e. share a common side)?
The first randomly chosen cell has
probability 4/64 = 1/16 of being a corner cell;
probability 24/64 = 3/8 of being a side cell;
probability 36/64 = 9/16 of being fully inside the board.
The respective conditional probabilities that the second randomly chosen cell is adjacent, with a common side, are:
2/63
3/63 = 1/21
4/63
The overall probability is then
1/16 * 2/63 + 3/8 * 1/21 + 9/16 * 4/63 = 1/18

Posted by Charlie
on 20160322 13:21:52 