HMMT November 2018 E10

Real numbers $x, y$ , and $z$ are chosen from the interval $[-1,1]$ independently and uniformly at random. What is the probability that

$|x|+|y|+|z|+|x+y+z|=|x+y|+|y+z|+|z+x| ?$

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{3}{8}

Solutions

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