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410 probability/intervals.p




Description

This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

410 probability/intervals.p


Given two random points x and y on the interval 0..1, what is the average
size of the smallest of the three resulting intervals?

probability/intervals.s

In between these positions the surface forms a series of planes.
Thus the volume under it consists of 2 pyramids each with an
altitude of 1/3 and an (isosceles triangular) base of area 1/2,
yielding a total volume of 1/9.

 

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