The probability
that
random arcs of angular size cover the circumference of a circle completely (for a circle
with unit circumference) is
where
is the floor function (Solomon 1978, p. 75).
This was first given correctly by Stevens (1939), although partial results were obtains
by Whitworth (1897), Baticle (1935), Garwood (1940), Darling (1953), and Shepp (1972).
The probability that arcs leave exactly gaps is given by
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Analysis, and in Stevens's Problem in Geometric Probability." Eugenics10,
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