Three points on a segment.
Given a real segment of length $L$ and a real number $d$ such that $0 \leq
d \leq L/2 $. Three points $x, y, z$ are chosen randomly on the segment.
Find the probability that $|x-y| \geq d, |x-z| \geq d$ and $|z-y| \geq d$.
I solved for the case when only $x$ and $y$ are given using simple
geometry, but I cannot draw a three-D image for this problem. Is there any
way to solve it analytically?
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