HMMT November 2013 U32

Guts
Answer

Suppose that $x$ and $y$ are chosen randomly and uniformly from $(0,1)$ . What is the probability that $\left\lfloor\sqrt{\frac{x}{y}}\right\rfloor$ is even?

Dataset text NuminaMath olympiads. Quoted with source.

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1-\frac{\pi^{2}}{24}

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