The probability lifesaver : all the tools you need to understand chance /
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Language Notes: | In English. |
| Published: |
Princeton :
Princeton University Press,
[2017]
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| Series: | Princeton lifesaver study guide.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- 2.2 Set Theory Review2.2.1 Coding Digression; 2.2.2 Sizes of Infinity and Probabilities; 2.2.3 Open and Closed Sets; 2.3 Outcome Spaces, Events, and the Axioms of Probability; 2.4 Axioms of Probability; 2.5 Basic Probability Rules; 2.5.1 Law of Total Probability; 2.5.2 Probabilities of Unions; 2.5.3 Probabilities of Inclusions; 2.6 Probability Spaces and [sigma]-algebras; 2.7 Appendix: Experimentally Finding Formulas; 2.7.1 Product Rule for Derivatives; 2.7.2 Probability of a Union; 2.8 Summary; 2.9 Exercises; 3 Counting I: Cards; 3.1 Factorials and Binomial Coefficients
- Cover; Title; Copyright; CONTENTS; Note to Readers; How to Use This Book; I General Theory; 1 Introduction; 1.1 Birthday Problem; 1.1.1 Stating the Problem; 1.1.2 Solving the Problem; 1.1.3 Generalizing the Problem and Solution: Efficiencies; 1.1.4 Numerical Test; 1.2 From Shooting Hoops to the Geometric Series; 1.2.1 The Problem and Its Solution; 1.2.2 Related Problems; 1.2.3 General Problem Solving Tips; 1.3 Gambling; 1.3.1 The 2008 Super Bowl Wager; 1.3.2 Expected Returns; 1.3.3 The Value of Hedging; 1.3.4 Consequences; 1.4 Summary; 1.5 Exercises; 2 Basic Probability Laws; 2.1 Paradoxes
- 3.1.1 The Factorial Function3.1.2 Binomial Coefficients; 3.1.3 Summary; 3.2 Poker; 3.2.1 Rules; 3.2.2 Nothing; 3.2.3 Pair; 3.2.4 Two Pair; 3.2.5 Three of a Kind; 3.2.6 Straights, Flushes, and Straight Flushes; 3.2.7 Full House and Four of a Kind; 3.2.8 Practice Poker Hand: I; 3.2.9 Practice Poker Hand: II; 3.3 Solitaire; 3.3.1 Klondike; 3.3.2 Aces Up; 3.3.3 FreeCell; 3.4 Bridge; 3.4.1 Tic-tac-toe; 3.4.2 Number of Bridge Deals; 3.4.3 Trump Splits; 3.5 Appendix: Coding to Compute Probabilities; 3.5.1 Trump Split and Code; 3.5.2 Poker Hand Codes; 3.6 Summary; 3.7 Exercises
- 4 Conditional Probability, Independence, and Bayes' Theorem4.1 Conditional Probabilities; 4.1.1 Guessing the Conditional Probability Formula; 4.1.2 Expected Counts Approach; 4.1.3 Venn Diagram Approach; 4.1.4 The Monty Hall Problem; 4.2 The General Multiplication Rule; 4.2.1 Statement; 4.2.2 Poker Example; 4.2.3 Hat Problem and Error Correcting Codes; 4.2.4 Advanced Remark: Definition of Conditional Probability; 4.3 Independence; 4.4 Bayes' Theorem; 4.5 Partitions and the Law of Total Probability; 4.6 Bayes' Theorem Revisited; 4.7 Summary; 4.8 Exercises; 5 Counting II: Inclusion-Exclusion
- 5.1 Factorial and Binomial Problems5.1.1 "How many" versus "What's the probability"; 5.1.2 Choosing Groups; 5.1.3 Circular Orderings; 5.1.4 Choosing Ensembles; 5.2 The Method of Inclusion-Exclusion; 5.2.1 Special Cases of the Inclusion-Exclusion Principle; 5.2.2 Statement of the Inclusion-Exclusion Principle; 5.2.3 Justification of the Inclusion-Exclusion Formula; 5.2.4 Using Inclusion-Exclusion: Suited Hand; 5.2.5 The At Least to Exactly Method; 5.3 Derangements; 5.3.1 Counting Derangements; 5.3.2 The Probability of a Derangement; 5.3.3 Coding Derangement Experiments