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I have 99 identical square tiles, each with a quarter-circle drawn on it like this:

 



When I arrange the tiles in a 9x11 rectangular grid, each with a random orientation, what is the expected value of the number of full circles I form?

 Aug 5, 2021
 #1
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The expected value is 9/32.

 Aug 5, 2021
 #2
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20 full circles smiley

 Aug 5, 2021

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