Geometric probability · Carnival game · difficulty 2 of 5
Coin on the tiles
At a carnival booth you toss a coin 1 inch across onto a large floor of square tiles, each 3 inches on a side. The coin lands flat at a uniformly random position. Treat the lines between tiles as having no width. What is the probability that the coin lies entirely within one tile, touching no line?
Answer with a probability. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.
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