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Neighbors or not? (Posted on 2016-03-22) Difficulty: 2 of 5
If two cells are chosen randomly on a 8x8 chessboard what is the probability that they are neighbors (i.e. share a common side)?

No Solution Yet Submitted by Ady TZIDON    
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Solution solution | Comment 1 of 3
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 2016-03-22 13:21:52
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