CEMC Cayley, 2010

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer Canada

A coin that is 8 cm in diameter is tossed onto a 5 by 5 grid of squares each having side length 10 cm. A coin is in a winning position if no part of it touches or crosses a grid line, otherwise it is in a losing position. Given that the coin lands in a random position so that no part of it is off the grid, what is the probability that it is in a winning position?

(A) $\frac{25}{441}$ (B) $\frac{1}{25}$ (C) $\frac{1}{49}$ (D) $\frac{5}{147}$ (E) $\frac{4\pi}{25}$

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