The classical probability theory has not crashed.
The hypotheses for the two requeriments presented by Atovigba, G.M.V.
in "Crash of classical probability theory" (
http://docs.google.com/
View?docid=dwhf8fx_0gst3xrnh) are incomplete. It is necessary to add
that the events (yi) must be independent. Considering independent
events the two requeriments are always true and no crash exists.
The events of having no faces 1,...,6 are not independent. For
instance, the event of not having 3 and the event of not having 4,
includes the cases of having 1, 2, 5 or 6 for both events. In a
representative polygon, this is simply the difference between: a) to
consider not intersecting areas (independent events); and b) to
consider intersecting areas (dependent events). The set of not
intersecting areas dividing the polygon have a total area equal to 1,
but the intersecting areas have not. The classical theory of
probability is very solid, and it uses particularly the measure theory
as a support in order to deal with all possible events.
On the contrary, the probabilistic sphere (hyper sphere) looks
undefined in relation with all the events and the following
calculations and inferences make no sense and do not prove anything.
Regards, Julio J.
___________________________________________________________________________________________________
On 3 dic, 09:25, "
mikeatovi...@gmail.com" <
mikeatovi...@gmail.com>
wrote: