Problem #151

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.

The solution will be posted shortly.

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