The main thesis advocated in the present paper is that some well-established laws of classical probability theory (typically the theorem of composite probabilities) are model dependent assertions, like some theorems of Euclidean geometry. In Sections (1) and (2) we briefly describe how this thesis is framed in the wider context of quantum probability and how it can throw some light on the open debate concerning the interpretation of quantum theory, as well as on the necessity of using a non-Kolmogorovian model in quantum theory. In Sections (3), (4) and (5) we show that the general ideas formulated in Sections (1) and (2), when given a precise mathematical form, allow one to account for all the nonstandard features of the quantum probability model (C -numbers, Hilbert spaces,... ) as well as to exhibit statistical models which are neither Kolmogorovian nor quantum.