olymmath

HMMT November 2022 U10

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A real number xx is chosen uniformly at random from the interval [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 .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{9}{10}

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