  We show that there is a non-empty class of finitely additive probabilities on
$\mathbb N^2$ such that for each member of the class, each set with limiting
relative frequency $p$ has probability $p$. Hence, in that context the
probability that two random integers are coprime is $6/\pi^2$. We also show
that two other interpretations of "random integer," namely residue classes and
shift invariance, support any number in $[0, 6/\pi^2]$ for that probability.
Finally, we specify a countably additive probability space that also supports
$6/\pi^2$.
