Suppose there exists an infinite number of equally spaced parallel green, yellow, red and blue lines, and we were to randomly toss a yellow colored needle whose length is less than or equal to the distance between adjacent lines. What is the probability that the needle will cross a yellow line?


closed as off-topic by Engineer Toast, Gamow, Beastly Gerbil, f'', Alexis Aug 12 '16 at 10:45

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  • "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – Engineer Toast, Gamow, Beastly Gerbil, f'', Alexis
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  • $\begingroup$ sounds like a math problem (Buffon's needle problem) for me. maybe even homework? $\endgroup$ – elias Aug 11 '16 at 14:55
  • $\begingroup$ Yes, elias, it's a variation of the Buffon's Needle Problem. It's not homework. $\endgroup$ – Ruben Gil Aug 11 '16 at 14:58

This is Buffon's Needle problem with $d=4l$ (from Mathworld).

so the probability is $\dfrac{1}{2\pi}$.


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