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Omni-MATH / 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|?

Problem

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problem

Real numbers x,yx, y, and zz are chosen from the interval [−1,1][-1,1] independently and uniformly at random. What is the probability that |x|+|y|+|z|+|x+y+z|=|x+y|+|y+z|+|z+x||x|+|y|+|z|+|x+y+z|=|x+y|+|y+z|+|z+x|?
Plain-text mathematical notation (without MathML)
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|?
Original LaTeX notation
Real numbers $x, y$, and $z$ are chosen from the interval $[-1,1]$ independently and uniformly at random. What is the probability that $|x|+|y|+|z|+|x+y+z|=|x+y|+|y+z|+|z+x|$?

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Source and history

task_id
22b95d0a-3290-5342-8579-94760cba5f6a
task_key
test--22b95d0a-3290-5342-8579-94760cba5f6a
task_revision_id
1
config / split
/ test

Official source

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