A rook and a bishop are placed at random on an 8x8 chess board. What is the probability that one will be attacking the other.
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Anonymous2007-10-07 16:20
Say they are placed 1 by 1.
If the rook is placed first, there is a 14/63 of the bishop being attacked by it.
There are 4 different possibilities corresponding for the bishop, for each layer of squares.
On the outer edge; it attacks 7
on the next 9, then 11, then 13
sum the chance of it being placed on each layer * the chance the rook is placed in it's range.
(196+180+132+52)/4032 +14/63 = 560/4032 + 14/63 = 1456/4032 = 13/36