Check out this thesis paper on "The Urinal Problem"...
Quote:
Abstract. A man walks into a men's room and observes n empty uri-
nals. Which urinal should he pick so as to maximize his chances of main-
taining privacy, i.e., minimize the chance that someone will occupy a
urinal beside him? In this paper, we attempt to answer this question
under a variety of models for standard men's room behavior. Our results
suggest that for the most part one should probably choose the urinal fur-
thest from the door (with some interesting exceptions). We also suggest
a number of variations on the problem that lead to many open problems
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http://people.scs.carleton.ca/~krana...ers/urinal.pdf