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Steve's kitchen floor has a tile pattern of square tiles of side length 10 cm. Steve drops a penny (which had radius 1 cm) on the floor. What is the probability that the penny lies entirely within one tile?

 Aug 12, 2019
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Nothing is mentioned about how many tiles make up the perimeter, where presumablly vertical walls restrict where the coin can land,

so I'll assume the question is equivalent to finding the probability that the coin lands entirely in a single tile.

 

Let's look at the case where the coin doesn't land entirely in the tile.  The coin center must land in a strip around the edge of the tile of width

r=1cm.  Thus in order to land entirely in the tile the coin center must land in a 10-2=8cm square.

 

Thus the probability is the ratio of this area over the entire tile area or p = 64/100 = 16/25

 Aug 12, 2019
edited by Rom  Aug 12, 2019

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