Question

A disc of unit radius is tossed at random onto a large rectangular floor, which is tiled with $4 \times 6$ tiles. Find the probability that the disc is contained entirely in a rectangular tile (and does not intersect the border between two tiles).

Answer 1

1/3

Explanation:

In order for the disc to be entirely contained in a rectangular tile, its center must be at least 1 unit from the nearest edge. Which means there's a 2 by 4 region that the center can lie in.

So the probability is (2×4) / (4×6) = 8/24 = 1/3.