  We review the well known Bertrand paradoxes, and we first maintain that they
do not point to any probabilistic inconsistency, but rather to the risks
incurred with a careless use of the locution "at random". We claim then that
these paradoxes spring up also in the discussion of the celebrated Buffon's
needle problem, and that they are essentially related to the definition of
(geometrical) probabilities on "uncountably" infinite sets. A few empirical
remarks are finally added to underline the difference between "passive" and
"active" randomness, and the prospects of any experimental decision
