Coin on the Tiles
A floor is covered with square tiles of side 1, separated by grout lines of negligible width. A coin of diameter 1/3 is tossed onto the floor so that its centre is uniformly distributed over the tile it lands on. What is the probability that the coin lies entirely inside a single tile, touching no grout line? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- Buffon's Needle 5.0/10
- An Obtuse Viewing Angle 5.0/10
- Rounding a Ratio 5.0/10
Source: Classic carnival-game exercise in geometric probability, in wide circulation; no traceable original source. Statement written for AxiomIQ.