Needle on parallel lines, problem

[mkkrnfoo85]

Hi, I was given a problem by the professor, and I feel like I do not know where to begin. Well, here is the problem:
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Endless, parallel East-to-West lines are spaced 2 inches apart on the ground, and a needle of length 1 inch is randomly tossed on the ground.
Compute the probability that the needle touches a line.
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I have tried attempting it, but I really don't have anywhere to start. Would anyone perhaps nudge me in the right direction? Thanks in advance.

-Mark

 

[ZioX]

This is a classical problem with a very interesting solution. There's a couple ways of doing it. Think about circles that spinning the needle generates...

 

[HallsofIvy]

One thing you will need to decide is: what is your random variable and what probability distribution will you use? It is probably simplest to assume a uniform distribution but what variable? The position of the center of the needle or one end point? The angle the needle makes with the horizontal? A combination of those?

 

[mkkrnfoo85]

ah thanks guys.

 

[tim_lou]

oh yeah nice problem, a classic one too... I won't spoil the fun but just do some geometry. In fact... I remember that there is like this one guy that does this experiment over and over and over... and over again to estimate a certain mathematical constant.

 

[ZioX]

oh yeah nice problem, a classic one too... I won't spoil the fun but just do some geometry. In fact... I remember that there is like this one guy that does this experiment over and over and over... and over again to estimate a certain mathematical constant.

And then fudged his results before publishing them, of course.

;0