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Omni-MATH / A real number x is chosen uniformly at random from the interval [0,1000]. Find the probability that ⌊(⌊(x)/(2.5)⌋)/(2.5)⌋=⌊(x)/(6.25)⌋.

Problem

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problem

A real number xx is chosen uniformly at random from the interval [0,1000][0,1000]. Find the probability that ⌊⌊x2.5⌋2.5⌋=⌊x6.25⌋\left\lfloor\frac{\left\lfloor\frac{x}{2.5}\right\rfloor}{2.5}\right\rfloor=\left\lfloor\frac{x}{6.25}\right\rfloor.
Plain-text mathematical notation (without MathML)
A real number x is chosen uniformly at random from the interval [0,1000]. Find the probability that ⌊(⌊(x)/(2.5)⌋)/(2.5)⌋=⌊(x)/(6.25)⌋.
Original LaTeX notation
A real number \(x\) is chosen uniformly at random from the interval \([0,1000]\). Find the probability that \(\left\lfloor\frac{\left\lfloor\frac{x}{2.5}\right\rfloor}{2.5}\right\rfloor=\left\lfloor\frac{x}{6.25}\right\rfloor\).

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Source and history

task_id
97c07b2a-8829-53e8-979e-2e4fc0bbc52a
task_key
test--97c07b2a-8829-53e8-979e-2e4fc0bbc52a
task_revision_id
1
config / split
/ test

Official source

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