Logarithmic Probability

Discrete Mathematics Level 2

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.