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.
Name:
Anonymous2007-10-07 15:10
11%
Name:
Anonymous2007-10-07 16:02
A gay person and a bishop are placed in an 8x8 feet room. What is the probability that one will be attacking the other?
Name:
Anonymous2007-10-07 16:07
4 points are chosen at random in a closed disk. What is the probability that they can be the vertices of a convex 4-gon?
Name:
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
Name:
4tran2007-10-15 2:31
>>4
That reminds me of an Olympiad question. Does anyone know the answer?
>>5
It's a good thing the two pieces cannot simultaneously attack each other. Still, the answer is good to a first approximation. The chance of the bishop being placed in any given layer depends on which layer the rook is in... Making this small adjustment is going to be a pain in the ass, so I'll neglect it for now.
>>6
What Olympiad? Let's see... Any three points choosen will form a triangle. The next point will either be outside this triangle, and the shape can be convex, or inside, and it can't.
So, what is the average area of a triangle from three random points in a closed disk? Dunno. Some sloppy simulation indicates about 0.231 on the unit circle, assuming uniform point distribution. Thus the answer should be approx. 1 - 0.231/π ≈ 0.93
>>9
Thanks. No wonder it seemed so familiar; I phailed this question last year!
Name:
Anonymous2007-10-25 20:50
pointless and gay as shit
Name:
Anonymous2007-10-26 16:57
Um, what? Since you can only attack an opponent if you land on his square, the chance is (1/64). For any given, unimportant block the first piece lands on, the second only has a 1 in 64 chance of being put on it.
Unless OP is bad at phrasing the question.
Name:
Anonymous2007-10-27 2:35
jews vs arabs??
Name:
Anonymous2007-10-27 7:08
>>12
he's not bad at phrasing the question, you're just stupid.