The "probability" of a "random" number $n$ to be prime is roughly $\frac{1}{\ln(n)}$.
Do we have a similar "probability" for a "random" number $n$ to be semiprime ?
I would already be content to have an estimate of the probability that the number has exactly two distinct prime factors. Can we perhaps exploit that $$\omega(n)$$ is roughly $$\ln(\ln(n))$$ with standard deviation $$\sqrt{\ln(\ln(n))}$$ ?
The sequence of semiprimes is the OEIS sequence A001358. The Formula section of the corresponding entry says that the $n$th semiprime is asymptotically equal to $n\log n/\log\log n$. This means that the interval $[1,n\log n/\log\log n]$ contains about $n$ semiprimes, so that the "probability" of a "random number" to be semiprime is asymptotically $\log\log n/\log n$.