Contents
- Chapter 1. Introduction
- Chapter 2. Some basic concepts
- Concept of an event
- Independence
- Expectation
- Calculation of simple probabilities
- Probability and odds
- Bayes Theorem
- Chapter 3. Counting methods
- Combinations and permutations
- Computation of permutations
- Computation of combinations
- How many aces are out?
- Chapter 4. Concept of a process
- Chapter 5. Some Paradoxes
- Chapter 6. Distributions
- Chapter 11. Mathematical aids to decision making
- Optimization Theory
- Decision Theory
- Game Theory
- Chapter 12. Psychology of Irrational Behavior
- Availability Error
- Chapter 15. Statistics
- What is statistics?
- Chapter 20. General Linear Model
- Basic model
- Influence
- Misc. topics
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Probability is a tool to guide your thinking
Probability theory is a tool to guide your thinking. It can help you evaluate decisions and risks. It can help you focus your thoughts on things that matter.
Think about it for a minute in terms of decisions and risk. Almost any decision you make in your life has potential consequences that range from good outcomes to bad outcomes. Important decisions can have potential consequences that range from very good outcomes to very bad outcomes. Certainly we want to avoid bad outcomes, a bad outcome is a consequence that we don’t want to face. But if we only make decisions that never have a potential bad outcome then we’ll probably never make a decision that ever has a very good outcome. That’s going to be a pretty boring life.
What probability does is let us replace the criteria of avoiding really bad potential consequences with a sense of different likelihoods of consequences. Probability is a way of categorizing those likelihoods into a framework. Rather than attaching importance to the severity of an outcome we can learn to attach importance based on how likely the outcome is to occur. Outcomes that are very unlikely to occur can be given less importance, even though they might involve severe consequences.
That’s actually not a natural way to think. Most people reading this probably already think that way to a degree at least, or you wouldn’t be interested enough in the subject to be reading it. But people have not always thought of the world in terms of probabilities or likelihoods. Some people still don’t think that way. The past is a guide to the future. But the past doesn’t determine the future. That’s an important concept that might seem obvious to you but wasn’t always so obvious to your ancestors.
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Alspach's Mathematics and Poker Page Brian Alspach used to write a regular column on combinatorics for Poker Digest. He's a retired math professor from Simon Fraser University. |
Tom Ferguson's home page He's a math ;professor at UCLA and Chris Ferguson's father. |
MathPages.com A collection of straight-forward introductions to various topics in mathematics and recreational mathematics. |
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