The SF Rule of Classical Probability: An Exploration of the "Gambler's Paradox"
DOI: 10.23977/jpms.2022.020101 | Downloads: 13 | Views: 659
Fei Yin 1
1 Institute of History of Science and Technology, Guangxi Minzu University, Nanning, Guangxi, 530006, China
Corresponding AuthorFei Yin
This paper uses the "gambler's paradox", an event of classical probability origin, as an entry point, and use graphical and observational methods to generalize the SF rule. The SF rule is used to explain the compound events, to demonstrate the formal guarantee of the SF rule, and to deduce the detailed steps of using the SF rule. As an important rule for selecting basic events in classical probability, the SF rule should be described in the probability foundation.
KEYWORDSClassical probability, basic events, SF rule, Sample space, Observational methods, Natural deduction
CITE THIS PAPER
Fei Yin, The SF Rule of Classical Probability: An Exploration of the "Gambler's Paradox". Journal of Probability and Mathematical Statistics (2022) Vol. 2: 1-8. DOI: http://dx.doi.org/10.23977/jpms.2022.020101.
 A. Vasudevan. (2017) Chance, determinism and the classical theory of probability, Studies in History and Philosophy of Science. 3, 1–12.
 A.W.F. Edwards. (1983) Pascal's problem: the 'Gambler's Ruin', International Statistical Review. 5, 73–79.
 B. Mates. (1986) The Philosophy of Leibniz: Metaphysics and Language, Oxford University Press, USA.11-13.
 G. Rodriguez. (2013) The Principles of Contradiction, Sufficient Reason, and Identity of Indiscernibles. Oxford Handbook of Leibniz, Oxford University Press, USA.27-29.
 I. Hacking. (2006) The Emergence of Probability: A Philosophical Study of Early Ideas about Probability, Induction and Statistical Inference, 2nd ed., Cambridge University Press, USA.15-17.
 L. E. Maistrov. (2014) Probability Theory: A Historical Sketch, Academic Press, USA.5-11.
 L.J. Daston. (1980) Probabilistic expectation and rationality in classical probability theory, Historia Mathematica. 3, 234–260.
 R. Durrett. (2007) Probability: Theory and Example, 3rd ed., World Book Publishing Company, Beijing.21-27.
 L. Xue. (2011) Probability Statistics Problems and Reflections, Science Press, Beijing.43-45.