An infinite number of (pairwise) parallel planes in space are arranged so that
the (perpendicular) distance between adjacent planes is *L*. A line segment
of length 1 is randomly placed in space (its midpoint and orientation being uniformly
distributed). What is the probability that the segment meets one of the planes?

Note that this is a generalization of the Buffon needle problem to three dimensions.

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The solution will be posted shortly.
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