According to the media,
in spring of this year
the experiment
CDF at Fermilab had made most likely
(``this
result has a 99.7 percent chance
of being correct''[1])
a great discovery
(``the most significant in physics
in half a century''[2]).
However, since the very beginning,
practically all particle physics
experts did not believe
that was the case. This is the last
of a quite long series of fake claims based
on trivial mistakes in the probabilistic reasoning
that can be sketched with the following
statements, understandable by everybody:
the probability of a senator to be a woman
is not the same as the probability of
a woman to be a senator;
a free neutron has only
probability
to decay after two hours, but, if we observe a neutron
decaying after such a time, this is not an indication
of an anomalous behavior of such a particle;
the fact that the probability of a Gaussian
random generator with and to
*produce* a number, rounded
to three decimal digits, equal to 3.000 is
does not allow us to say that, once this number
has been observed, there is only
probability
*it comes from* that generator, neither that
is the probability that 3.000 is a
*statistical fluctuation*;
and not even, still considering the latter
numerical example, we can say that
the probability of 3.000 to be a statistical
fluctuation is
, `*because*' this is
the probability of such
a generator to produce a number
*larger or equal* than the observed one.
The main purpose of this note is to invite everybody,
but especially journalists and general public, most times
innocent victims of misinformation of this kind,
to mistrust claims not explicitly reported
in terms of *how much we should
believe something*, under well stated conditions
and assumptions.
(A last minute appendix has been added, with comments
on the recent news concerning the Higgs at LHC.)

- Introduction
- The facts
- The (filtered and processed) data
- The statistically motivated claim
- How the claim was explained to the general public (and perhaps even what some particle physicist thought)

- Where is the problem?
- Why there is such a problem?

- The mathematics of beliefs
- Stating the strength of ``pragmatic beliefs'' by odds
- Coherent virtual bets
- Belief Vs imagination, beliefs Vs wish, subjective Vs arbitrary: the role of the coherent (virtual) bet
- Updating beliefs

- Conclusions
- Bibliography
- Appendix: `???' at Fermilab Vs Higgs boson at CERN
- About this document ...