Nothing is more basic than an axiomatic theory.
3.1 BASIC PROBABILITY THEORY
Girolamo Cardano (1501–1576) wrote the first known book on probability, entitled De Ludo Aleae (About Games of Chance). He was an Italian medical doctor and mathematician, and the book was published, in 1663, nine decades after his death. Cardano was a known card player, and the manuscript was a handbook on this subject, containing some discussion on probability.
The first mathematical treatise on probability theory, published in 1657, was written by the Dutch scientist Christian Huygens (1629–1695), a manuscript entitled De Ratiociniis in Ludo Aleae (About Reasoning in Games of Chance).
Abraham de Moivre (1667–1754) ...