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Jul 3 at 13:52 comment added Emil Jeřábek @Henry This should follow from the criterion in my answer.
Jul 3 at 12:34 comment added Henry I suspect there may be another sense in which it is less than $\frac12$. If you look at the proportion of those coprime $(n,k)$ with $n$ and $k$ bounded above by some $m$, then a experiment with various small $m$ suggests that the proportion leading to $2$ may be closer to $\frac13$ than to $\frac12$.
Jul 3 at 6:31 history answered Gerry Myerson CC BY-SA 4.0