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405.Same Binary Magnitude

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classical probabilityCh. 4 — Continuous Distributions and Moments444+ Problems in Probability
Let X,Y∼Unif(0,1)X, Y \sim \mathrm{Unif}(0,1) IID. Compute the probability that ⌊log⁡2X⌋=⌊log⁡2Y⌋\lfloor \log_2 X \rfloor = \lfloor \log_2 Y \rfloor.

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Same Binary Magnitude | Quant Practice