请帮忙看看这个数学题，谢谢

来源: 新手008 于 2023-08-11 17:18:48 [旧帖] [给我悄悄话] 本文已被阅读：次

I have $99$ identical square tiles, each with a quarter-circle drawn on it like this:
$[asy] size(1.5cm); draw(Arc((2,0),1,90,180),red+1); draw((0,0)--(2,0)--(2,2)--(0,2)--(0,0)); [/asy]$
When I arrange the tiles in a $9\times 11$ rectangular grid, each with a random orientation, what is the expected value of the number of full circles I form?