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"a needle of length l is dropped at random onto a sheet of paper ruled with parallel lines a distance l apart. what is the probability that the needle will cross a line?"

in the previous problem. i solved for the expectation values of theta, and its <x> projection. I'm thinking the solution will be a combination of the probabilities for theta, and also for where the needle falls on the y-axis (i.e. right on a line or somewhere between two lines) but i can't quite get a handle on the problem. any ideas?