Calculating The Probability of Events Using Logical Operations

Nishonboyev Azizbek  Solijonovich; Jarkinov Zarifjon  Umaraliyevich

Nishonboyev Azizbek Solijonovich Fergana State University, Senior Lecturer, Department of Mathematics
Jarkinov Zarifjon Umaraliyevich Fergana State University, Senior Lecturer, Department of Mathematics, PhD

Keywords: relay-contact schemes, logic operations, parallel and consecutively connect principles, phenomenon, reflection

Abstract

General Background: The merge between probability theory and mathematical logic introduces a useful analytical tool of uncertain events modeling in systems whose operations are described by logical conditions. Particular Background: Probabilistic dependencies are closely related to logical operations at conjunction and disjunction in relay-contact schemes and in electronic systems, which have a practical use in both engineering and teaching. Knowledge Gap: Nevermore, there has been low priority on the use of both logical operations and event analysis using probabilistic rules, specifically in teaching case. Objective: The objective of the following article is to find out how to use logical operations to figure out the likelihood of events and to investigate their application to circuit-based situations. Results: Based on classical probabilities and logical truth tables, the article discusses an illustration in which there are several connectors through which energy can flow. It concludes that in 7 out of 16 combinations the event will happen, the complementary logic of which confirms the conclusion. Further the distribution law of the working time of a lamp is calculated depending on the difference equations. Novelty: The treatment is a composition of probabilistic assessment and logic-based model. Implications: This technique has theoretical and practical relevance in the teaching of probability and examination of system reliability.

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