Question

A coin of radius $3	ext{ cm}$ is randomly dropped on a square floor full of square shaped tiles of side $10	ext{ cm}$ each. What is the probability that the coin will land completely within a tile? In other words, the coin should not cross the edge of any tile.

Accepted Answer

E. For the coin of radius $r = 3	ext{ cm}$ to land completely inside a square tile of side $s = 10	ext{ cm}$, its center must be at least $3	ext{ cm}$ away from each of the 4 edges of the tile. The valid region for the center of the coin is a smaller square of side length: $$10 - 2(3) = 4	ext{ cm}$$ $$	ext{Area of valid region} = 4 	imes 4 = 16	ext{ sq. cm}$$ $$	ext{Total area of a tile} = 10 	imes 10 = 100	ext{ sq. cm}$$ $$	ext{Probability} = \frac{16}{100} = 0.16$$ Thus, Option E is correct.

Probability of Coin inside Square Tile

Explanation

Practise this under exam conditions