Frank has a tablecloth covered with 1 cm diameter black polka dots. The polka dots form a square grid with 2 cm between neighboring centers.
He takes a flat 4 cm by 4 cm piece of clear plastic and paints four 1 cm diameter circles on it in the same pattern as on the tablecloth. After laying the tablecloth on a flat surface, he randomly tosses the piece of plastic onto it.
To three significant figures, what is the probability that none of the polka dots on the plastic will overlap any portion of any of the polka dots on the tablecloth?
This problem reminds me of Throwing Needles, pid=2794.
In that problem, and in a similar problem I recall doing in a class in college, the analytic solution had pi in the denominator.
I wonder if pi is in the denominator for this problem.
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Posted by Larry
on 2024-12-17 12:12:57 |