Understanding Probability and Its Role in Decision Making

Frederic G. Snider, RPG and Michelle B. Snider, PhD

Course Outline

This 3 hour course provides the non-mathematician the basic concepts and tools used in Probability Theory, with particular emphasis on the impacts to the decision making process. Background information, such as key definitions with examples, is provided, as well as real-world applications. Some of the important non-intuitive and counter-intuitive lessons of probability theory are presented, including the concepts of random walks, game theory, the psychology of rarity and the psychology of randomness. The application of probability in many basic fields, including physics and medicine are discussed.

This course is a companion to, and predecessor for, our other course entitled “Understanding Statistics -, What It Is, Its Proper Use, and Its Widespread Misuse”, which builds upon the probability discussions here.

The course includes a multiple-choice quiz at the end, which is designed to enhance the understanding of the course materials.

Learning Objectives

The learning objectives for this course are:

• Understanding the basic concepts underlying Probability Theory;
• Learning the definition of key terms used to discuss probability;
• Understanding a few of the key axioms and formulas commonly used;
• Learning the difference between discrete, conditional and Bayesian probability;
• Ability to apply probabilistic concepts to decision making;
• Understanding the widespread application of probability theory;
• Recognizing the proper use and mis-use of probabilistic terms by others;
• Recognizing the importance of probability in science and public policy; and
• Developing a base for advancing to courses on Statistics.

Intended Audience

This course is intended for non-mathematicians who have an interest in understanding (or re-learning) the fundamentals of probability, learning how probabilitistic approaches are becoming more and more common in both the sciences and public policy, and/or interested in advancing to higher-level  courses providing a better understanding of statistics.

Benefit to Attendees

All engineers, architects, and related fields can benefit from a better understanding of probability theory and its widespread application to all of our daily lives, from decision making to risk analysis, to improving our understanding and communication of uncertainty and randomness.

Course Introduction

The opening credits to the popular crime-solving TV series "NUMB3RS" include the statement that "We all use math every day; to predict weather, to tell time, to handle money. Math is more than formulas or equations; it's logic, its rationality, it's using your mind to solve the biggest mysteries we know."

Sometimes those numbers are concrete values, as in "The speed limit is 35" or "It is currently 68 degrees outside." But often, the numbers we see are not fixed, but rather are probabilities of future outcomes. We often use the phrase “I’ll take my chances.” But what does that really mean? Should our ‘gut feeling’ really guide our pick of lottery numbers? Or investment portfolios? Or career choices?

When most people think of probability, they think of games of chance: poker, roulette, etc. Much of the early mathematics of probability was developed for such games. However, we now realize that much of the world around us is probability -based.  For example, the certainties of classical physics have given way to the probabilistic models of quantum mechanics and thermodynamics. In biology, we now understand genetics and evolution in a context of random behavior. These views represent major paradigm shifts.  Closer to home, probability is pervasive in our everyday lives:

 Weather Forecasting Disaster Preparedness Life and Homeowners Insurance Uses of Technology Medicine and Consumer-Driven Care Personal, Home and National Security Finance and Retirement Planning Education TV Game Shows Real Estate Sports Foreign Travel Diet and Exercise Etc. etc. etc

Our lives are full of situations with unknown outcomes, whether we like it or not. While we usually cannot get rid of the uncertainty, what we can do is try to deal with the uncertainty in some sort of methodical or rational way.

Course Content

In this lesson, you are required to download and study the following course content:

Please click on the above underlined hypertext to view, download or print the document for your study.

Course Summary

Probability Theory has its roots in determining odds for games of chance. But as time goes on, Probability Theory has found its way into many fields. It already plays a fundamental role in our understanding of the physical world around us, from biology to physics to our health and our stock portfolios. Randomness and uncertainty are everywhere, and probability gives us a quantitative way to deal with them in such a way that we can make informed decisions. At best, probability often confronts us with counterintuitive ideas that make us re-evaluate what we think we know. And at worst, just because we make a ‘good’ decision based on a probabilistic analysis, doesn't mean we won’t be disappointed at the actual outcome.

One major application of probability that we’ve skipped here is in the field of statistics. One can make a probabilistic model of what one might expect from an experiment, and then compare that to a given a set of data. If there is a large difference between them, you go back and change your model accordingly. The use of probability in statistics is covered in another of our courses: Understanding Statistics -, What it is, Its Proper Use, and Its Widespread Misuse.

Quiz

Once you finish studying the above course content, you need to take a quiz to obtain the PDH credits.

DISCLAIMER: The materials contained in the online course are not intended as a representation or warranty on the part of PDH Center or any other person/organization named herein. The materials are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered architect and/or professional engineer/surveyor. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.