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Omni-MATH / Three real numbers x,y,z are chosen randomly, and independently of each other, between 0 and 1, inclusive. What is the probability that each of x−y and x−z is greater than −(1)/(2)…

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problem

Three real numbers x,y,zx, y, z are chosen randomly, and independently of each other, between 0 and 1, inclusive. What is the probability that each of x−yx-y and x−zx-z is greater than −12-\frac{1}{2} and less than 12\frac{1}{2}?
Plain-text mathematical notation (without MathML)
Three real numbers x,y,z are chosen randomly, and independently of each other, between 0 and 1, inclusive. What is the probability that each of x−y and x−z is greater than −(1)/(2) and less than (1)/(2)?
Original LaTeX notation
Three real numbers $x, y, z$ are chosen randomly, and independently of each other, between 0 and 1, inclusive. What is the probability that each of $x-y$ and $x-z$ is greater than $-\frac{1}{2}$ and less than $\frac{1}{2}$?

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Source and history

task_id
6537ec12-f101-5e25-95fe-9603782f0766
task_key
test--6537ec12-f101-5e25-95fe-9603782f0766
task_revision_id
1
config / split
/ test

Official source

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