Conditional Prevision and Probability

Abstract

This chapter examines how, for all the events (E), and random quantities (X), of interest, one passes from probabilities (P(E)), and previsions (P(X)), to those conditional on a given event (H). It presents discussion that leads to an understanding of how it should be possible to pass from the initial probabilities to the final ones through intermediate stages. The probability of E conditional on H, probability ‘of the event E conditional on the event H’ (P(E|H)), can be either equal to P(E), or greater, or less. Without any intention of becoming theoretical, informally, stochastic dependence in the direct sense, the case that arises in the most evident form, and in the most obvious and common examples in treatments from all conceptual viewpoints. This is the case in which the occurrence of an event changes the circumstances surrounding the occurrence of another one.

Cite this paper

@incollection{definetti2017conditional,
  title = {{Conditional Prevision and Probability}},
  author = {de Finetti, Bruno and Machì, Antonio and Smith, A. F. M.},
  booktitle = {Wiley series in probability and statistics},
  pages = {113--152},
  year = {2017},
  doi = {10.1002/9781119286387.ch4}
}

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