MathNet 2018-part-07 — 177 problems (EN–VI) Question 41

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

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