See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/257820702 Understanding and Calculating the Odds: Probability Theory Basics and Calculus Guide for Beginners, with Applications in Games of Chance and Eve.... Book * May 2006 CITATIONS 0 READS 487 1 author: Some of the authors of this publication are also working on these related projects: Metatheoretical analysis and structural alternatives of the resolving of the philosophical problem of the applicability of mathematics in natural sciences and Wigner's puzzle View project Editing/Proofreading/Commenting/Research Designing in philosophy of science/philosophy of mathematics Collaboration and co-authorship View project Catalin Barboianu University of Bucharest 27 PUBLICATIONS 5 CITATIONS SEE PROFILE All content following this page was uploaded by Catalin Barboianu on 04 March 2016. The user has requested enhancement of the downloaded file. UNDERSTANDING AND CALCULATING THE ODDS Probability Theory Basics and Calculus Guide for Beginners, with Applications in Games of Chance and Everyday Life This is a sample containing the title page, copyright page and content list. There is no electronic edition of this book. The printed edition can be ordered at minimal price at http://probability.infarom.ro/books.html . Cătălin Bărboianu ∏  2 INFAROM Publishing Pure and applied mathematics office@infarom.com http://www.infarom.com http://books.infarom.ro http://probability.infarom.ro ISBN-10 9738752019 ISBN-13 9789738752016 Publisher: INFAROM Author and translator: Cătălin Bărboianu Correction editor: Sara M. Stohl Mathematics subject classification (2000): 00A05, 00A07, 00A08, 00A30, 03A05, 03C95, 60A05, 60A10, 60A99, 65C50, 65C99. Copyright © INFAROM 2008 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of tables, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of Copyright Laws and permission for use must always be obtained from INFAROM. 3 Contents Introduction ..................................................................... What Is Probability? .......................................................... Words and concepts .................................................... Mathematical models .................................................. "Probability" – the word ............................................. The concept of probability .......................................... Probability as a limit ........................................................ Experiments, events .................................................... Relative frequency ...................................................... Probability as a measure .................................................. Relativity of probability .................................................. The hazard ................................................................. Infinity ........................................................................ Conceptual and applicability relativities .................... Philosophy of probability ................................................ Prediction .................................................................... Frequency ................................................................... Possibility ................................................................... Psychology of probability ................................................ Probability Theory Basics ................................................. Fundamental notions ....................................................... Sets .............................................................................. Functions ..................................................................... Boole algebras ............................................................ Sequences of real numbers. Limit .............................. Series of real numbers ................................................ Measure theory basics ..................................................... Sequences of sets ........................................................ Tribes. Borel sets. Measurable space .......................... Measure ....................................................................... Field of events. Probability .............................................. Field of events ............................................................. Probability on a finite field of events ......................... Probability properties ................................................. Probability σ -field ..................................................... Independent events. Conditional probability .............. Total probability formula. Bayes's theorem ........ 5 13 14 22 28 33 34 38 40 46 63 63 68 72 78 79 83 87 93 113 114 114 116 118 120 126 127 128 129 132 135 137 143 147 152 154 156 4 Law of large numbers ................................................. Discrete random variables .......................................... Moments of a discrete random variable ................. Distribution function .............................................. Discrete classical probability repartitions .............. Bernoulli scheme ............................................... Poisson scheme ................................................. Polynomial scheme ........................................... Scheme of non-returned ball ............................. Convergence of sequences of random variables .... Law of large numbers ....................................... Combinatorics ..................................................................... Permutations .................................................................... Arrangements .................................................................. Combinations ................................................................... Combinatorial calculus .................................................... Direct application of formulas .................................... Partitioning combinations ........................................... Applications ..................................................................... Solved applications ..................................................... Unsolved applications ................................................. Beginner's Calculus Guide ................................................ Introduction .......................................................... The general algorithm of solving .................................... Framing the problem ................................................... Exercises and problems .......................................... Establishing the theoretical procedure ........................ Methods of solving ................................................ Exercises and problems ..................................... Selecting the formulas to use ................................. The list of formulas to use ................................. Exercises and problems ..................................... The calculus ................................................................ Odds and probability .............................................. Exercises and problems .......................................... Probability Calculus Applications .................................... Solved applications .......................................................... Unsolved applications ..................................................... References ............................................................................ 157 159 164 168 169 169 171 173 174 175 177 179 179 180 181 182 183 187 191 191 205 209 209 213 214 219 227 227 228 234 234 239 246 247 248 263 264 282 299 View publication stats