h*****i
发帖数: 64 | 1 What is the probability that a quarter flipped onto a chess board will touch
4 corners?
难道就是4/64 = 1/16？
多谢 | l****u
发帖数: 34 | 2 I think it depends on the ratio between area of quarter and area of one
block of chess board. You need to consider where the center of quarter could
be. Probably it is a circle. Then you can calculate probability. | f********k
发帖数: 136 | 3 If we simply assume the center of the coin will be located within the
chessboard, The center of the coin will be uniformly distributed on a 8*8
square. The coin will touch one of the corners only if the distance between
the center of the coin and the corner is less than the radius of the coin,
which form 4 quarter circles with radius r on the four corners. The areas of
these 4 quarter circles simply sum to pi*r^2. So the probability will be pi
*r^2/64, where r is the radius of coin.
However, if the center of coin can be outside the square, you need to
enlarge the square by a distance of r at every boundaries, which will be a
special square with four round corners. The probability will be the ratio of
areas of 4 circles to the total area. My calculation gives 4pi*r^2/(64+32r+
pi*r^2).
touch
【在 h*****i 的大作中提到】
: What is the probability that a quarter flipped onto a chess board will touch
: 4 corners?
: 难道就是4/64 = 1/16？
: 多谢
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