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Let square of size $10\times 10$ is divided into two $5\times10$ rectangles: A and B. Toss a coin with radius $1$ into the square. What's the probability that the coin is completely in A?

I have no idea about this problem. I even don't know what's the sample space. Can anyone guide me how I can go on?

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In some problems in geometric probability, there can be quite different answers depending on one's hoice of sample space. Hard to know what is natural here. Maybe centre of square uniform on the inner $8\times 8$ square. –  André Nicolas Nov 6 '12 at 2:12
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1 Answer

I'm going to assume that by tossing a coin into the square, they want the coin completely in the square. Consider where the center of the penny could land and still be within rectangle A. It can't land within a radius length of a boundary without some part of the coin overhanging it, so the area that the center of the coin can land in such that the coin is completely in A would be $3\times8$, or 24.

So, to finish the problem, I'd try calculating the area the center of the coin could land and still remain in the square. The probability would be the ratio of the 2 areas.

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oops. Was thinking diameter 1 for some reason. Corrected. –  Mike Nov 6 '12 at 12:00
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