A Full Description of All Commutative Associative Polynomial Operations on Probabilities

Authors

Miroslav Svitek, Czech Technical University in PragueFollow
Olga Kosheleva, University of Texas at El PasoFollow
Vladik Kreinovich, University of Texas at El PasoFollow
Nguyen Hoang Phuong, Thang Long UniversityFollow

Publication Date

9-1-2024

Comments

Technical Report: UTEP-CS-24-46

Abstract

When two events are independent, the probability that both events occur is equal to the product p1 * p2 of the probabilities of each of these events. The probability that at least one of these events will occur is equal to p1 + p2 − p1 * p2. In both cases, we have a commutative associative polynomial operation. A natural question is: how can we describe all possible operations of this type? These operations are described in this paper.