  Classical statistics and Bayesian statistics refer to the frequentist and
subjective theories of probability respectively. Von Mises and De Finetti, who
authored those conceptualizations, provide interpretations of the probability
that appear incompatible. This discrepancy raises ample debates and the
foundations of the probability calculus emerge as a tricky, open issue so far.
Instead of developing philosophical discussion, this research resorts to
analytical and mathematical methods. We present two theorems that sustain the
validity of both the frequentist and the subjective views on the probability.
Secondly we show how the double facets of the probability turn out to be
consistent within the present logical frame.
