  In 1931 de Finetti proved what is known as his Dutch Book Theorem. This
result implies that the finite additivity {\it axiom} for the probability of
the disjunction of two incompatible events becomes a {\it consequence} of de
Finetti's logic-operational consistency notion. Working in the context of
boolean algebras, we prove de Finetti's theorem. The mathematical background
required is little more than that which is taught in high school. As a
preliminary step we prove what de Finetti called ``the Fundamental Theorem of
Probability'', his main contribution both to Boole's probabilistic inference
problem on the object of probability theory, and to its modern reformulation
known as the optimization version of the probabilistic satisfiability problem.
In a final section, we give a self-contained combinatorial proof of de
Finetti's exchangeability theorem.
