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Omni-MATH / Three points are chosen inside a unit cube uniformly and independently at…

Problem

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problem

Three points are chosen inside a unit cube uniformly and independently at random. What is the probability that there exists a cube with side length 12\frac{1}{2} and edges parallel to those of the unit cube that contains all three points?
Plain-text mathematical notation (without MathML)
Three points are chosen inside a unit cube uniformly and independently at random. What is the probability that there exists a cube with side length (1)/(2) and edges parallel to those of the unit cube that contains all three points?
Original LaTeX notation
Three points are chosen inside a unit cube uniformly and independently at random. What is the probability that there exists a cube with side length $\frac{1}{2}$ and edges parallel to those of the unit cube that contains all three points?

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Source and history

task_id
f089d423-72c1-5846-99ed-260335d73e94
task_key
test--f089d423-72c1-5846-99ed-260335d73e94
task_revision_id
1
config / split
/ test

Official source

initial import