Probability Fundamentals & Geometric Probability · Challenge problem

A floor is covered with square tiles of side $5$ cm, so the grout lines form a square grid with spacing $5$ cm. A coin of diameter $2$ cm is dropped so that its centre lands uniformly at random. What is the probability that the coin crosses exactly one grout line? (Treat grout lines as having no width; a coin that touches a line counts as crossing it.) Express your answer as a common fraction.