# Logarithmic Probability

If you pick a number $$x$$ uniformly at random on the interval $$[0,1],$$ what is the probability that $$\left\lfloor \log _{2}\frac{1}{x}\right\rfloor$$ is odd, to 3 significant figures?

Note: $$\lfloor \cdot \rfloor$$ is the floor function.

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