What Are the Chances? Probability Made Clear

Course No. 1474
Professor Michael Starbird, Ph.D.
The University of Texas at Austin
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Course No. 1474
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Course Overview

Life is full of probabilities. Every time you choose something to eat, you deal with probable effects on your health. Every time you drive your car, probability gives a small but measurable chance that you will have an accident. Every time you buy a stock, play poker, or make plans based on a weather forecast, you are consigning your fate to probability.

What Are the Chances? Probability Made Clear helps you understand the random factors that lurk behind almost everything—from the chance combinations of genes that produced you to the high odds that the waiting time at a bus stop will be longer than the average time between buses if they operate on a random schedule.

In 12 stimulating half-hour lectures, you will explore the fundamental concepts and fascinating applications of probability.

High Probability You Will Enjoy This Course

Professor Michael Starbird knows the secret of making numbers come alive to non-mathematicians: he picks intriguing, useful, and entertaining examples. Here are some that you will explore in your investigation of probability as a reasoning tool:

  • When did the most recent common ancestor of all humans live? Applying probabilistic methods to the observed mutation rate of human genetic material, scientists have traced our lineage to a female ancestor who lived about 150,000 years ago.
  • How much should you pay for a stock option? Options trading used to be tantamount to gambling until about 1970, when two economists, Fischer Black and Myron Scholes, found a method to quantify those risks and to create a rational model for options pricing.
  • What do you do on third down with long yardage? In football, a pass is the obvious play on third down with many yards to go. Of course, the other team knows that. Probability and game theory help decide when to run with the ball to keep your opponent guessing.

What You Will Learn

The course literally begins with a roll of the dice, as Professor Starbird demonstrates that games of chance perfectly illustrate the basic principles of probability, including the importance of counting all possible outcomes of any random event. In Lecture 2, you probe the nature of randomness, which is famously symbolized by monkeys randomly hitting typewriter keys and creating Hamlet. In Lecture 3, you explore the concept of expected value, which is the average net loss or gain from performing an experiment or playing a game many times. Then in Lecture 4, you investigate the simple but mathematically fertile idea of the random walk, which may seem like a mindless way of going nowhere but which has important applications in many fields.

After this introduction to the key concepts of probability, you delve into the wealth of applications. Lectures 5 and 6 show that randomness and probability are central components of modern scientific descriptions of the world in physics and biology. Lecture 7 looks into the world of finance, particularly probabilistic models of stock and option behavior. Lecture 8 examines unusual applications, including game theory, which is the study of strategic decision-making in games, wars, business, and other areas. Then in Lecture 9 you consider two famous probability puzzles guaranteed to cause a stir: the birthday problem and the Let's Make a Deal® Monty Hall question.

Finally, Lectures 10–12 cover increasingly sophisticated and surprising results of probabilistic reasoning associated with Bayes theorem. The course concludes with probability paradoxes.

Take the Weather Forecasting Challenge

One of the most familiar experiences of probability that we have on a daily basis is the weather report, with predictions like, "There is a 30 percent chance of rain tomorrow." But what does that mean? What do you think? Choose one:

  • (a) Rain will occur 30 percent of the day.
  • (b) At a specific point in the forecast area, for example, your house, there is a 30 percent chance of rain occurring.
  • (c) There is a 30 percent chance that rain will occur somewhere in the forecast area during the day.
  • (d) 30 percent of the forecast area will receive rain, and 70 percent will not.
  • (e) None of the above.

In Lecture 5, Dr. Starbird puts this particular forecast under the microscope to demonstrate that probabilistic statements have very precise meanings that can easily be misinterpreted—or misstated. He explains why the answer is (e) and not one of the other choices. He also explains why the official definition from the National Weather Service is subtly but decidedly wrong.

He even wagers that within five years the phrasing of the official definition will change because somebody at the National Weather Service will hear this lecture!

Games People Play

The formal study of probability was born at the dice table. Gambling continues to provide instructive examples of the principles of chance and probability, including:

  • Gambler's ruin: A random walk is a sequence of steps in which the direction of each step is taken at random. In gambling, the phenomenon assures that a bettor who repeatedly plays the same game with even odds will eventually—and invariably—go broke.
  • St. Petersburg paradox: A famous problem in probability involves a hypothetical game supposedly played at a casino in St. Petersburg. Though simple and apparently moderately profitable for the gambler, the expected value of the game is infinite! Yet no reasonable person would pay very much to play it. Why not?
  • Gambler's addiction: Randomness plays a valuable role in reinforcing animal behavior. Changing the reinforcement in an unpredictable, random way leads to behaviors that are retained for a long time, even in the absence of rewards. Applied to humans, this observation may help explain the compulsiveness of some gamblers.

Probability to the Rescue

One approach to probability, developed by mathematician and Presbyterian minister Thomas Bayes in the 18th century, interprets probability in terms of degrees of belief. As new information becomes available, the calculation of probability changes to take account of the new data. The Bayesian view reflects the reality that we adjust our confidence in our knowledge as we gain evidence.

The world of fluctuating probabilities, under continual adjustment as new evidence comes to light, captures the way the world works in realms like medicine, where a physician makes a preliminary diagnosis based on symptoms and probabilities, then orders tests, and then refines the diagnosis based on the test results and a new set of probabilities.

If you think about it, it's also the way you work when you're on a jury. At the outset, you have a vague impression of the likelihood of guilt or innocence of the defendant. As evidence mounts, you adjust the relative probabilities you assign to each of these verdicts. You may not do a formal calculation, but your informal procedure is nonetheless Bayesian.

Randomness is all around us. "Many or most parts of our lives involve situations where we don't know what's going to happen,"; says Professor Starbird. Probability comes to the rescue to describe what we should expect from randomness. It is a powerful tool for dispelling illusions and uncertainty to help us understand the true odds when we roll the dice in the game of life.

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12 lectures
 |  Average 30 minutes each
  • 1
    Our Random World—Probability Defined
    The concept of randomness and its quantification through probability is central to understanding the world of science, games, business, and other endeavors. This lecture introduces the basic laws of probability. x
  • 2
    The Nature of Randomness
    Randomness refers to situations in which given results are unpredictable, but a large enough collection of results is predictable. The goal of probability is to describe what it is to be expected from randomness. x
  • 3
    Expected Value—You Can Bet on It
    Expected value is a useful measure for making decisions about probabilistic outcomes. It provides a numerical way to judge whether to bet on a particular game or make a particular investment. x
  • 4
    Random Thoughts on Random Walks
    A random walk is a description of random fluctuations. It aids the analysis of situations ranging from counting votes to charting pollen on a fishpond, and it explains the sad fate of persistent bettors. x
  • 5
    Probability Phenomena of Physics
    Quantum mechanics describes the location of subatomic particles as a probability distribution. Weather predictions also give probabilistic descriptions; but what is the meaning of a statement like "There is a 30 percent chance of rain tomorrow"? x
  • 6
    Probability Is in Our Genes
    Because randomness is centrally involved in passing down genetic material, probability can be used to model the distribution of genetic traits and to describe how traits of whole populations alter through a random process called genetic drift. x
  • 7
    Options and Our Financial Future
    By characterizing the expected behavior of a stock in the future and describing a probability distribution of its likely future price, mathematicians can quantify sophisticated risks in options contracts. However, the practice can be a very dangerous game. x
  • 8
    Probability Where We Don't Expect It
    What does probability have to do with determining if a number is prime, or deciding football strategy, or training animals? More than you might think—probability often plays a central role where we least expect it. x
  • 9
    Probability Surprises
    No course on probability could be complete without a discussion of two of the most famous examples of counterintuitive probabilistic scenarios: the birthday problem and the Let's Make a Deal® Monty Hall question. x
  • 10
    Conundrums of Conditional Probability
    Conditional probability refers to a situation where the probability of one event is affected by some other event or piece of information. Principles of dealing correctly with conditional probability are tricky and highly nonintuitive. x
  • 11
    Believe It or Not—Bayesian Probability
    This lecture looks at probability from a different point of view: namely, probability associated with measuring a level of belief as opposed to measuring the frequency with which the results of a random process occur. This is the Bayesian view of probability. x
  • 12
    Probability Everywhere
    A pair of paradoxes shows the power of the Bayesian approach in analyzing counterintuitive cases in probability. The course concludes with a review of the topics covered and the importance of probability in our world. x

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  • 12 lectures on 2 DVDs
  • 88-page printed course guidebook
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Course Guidebook Details:
  • 88-page printed course guidebook
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Your professor

Michael Starbird

About Your Professor

Michael Starbird, Ph.D.
The University of Texas at Austin
Dr. Michael Starbird is Professor of Mathematics and University Distinguished Teaching Professor at The University of Texas at Austin, where he has been teaching since 1974. He received his B.A. from Pomona College in 1970 and his Ph.D. in Mathematics from the University of Wisconsin-Madison in 1974. Professor Starbird's textbook, The Heart of Mathematics: An Invitation to Effective Thinking, coauthored with Edward B. Burger,...
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What Are the Chances? Probability Made Clear is rated 3.7 out of 5 by 75.
Rated 5 out of 5 by from Adding essential components to my understanding. I was initially skeptical because of other reviews but I was pleasantly surprised by this course since it supplemented my understanding of the probability. Professor Michael brought great clarity and energy his lectures, this course have filled a necessary void which was hard to plug without a tutor or in person mentor. It was a very cheap course for a very scarce topic. I will definitely take more courses from this professor, wish it was a longer course. I will keep coming back to this series again and again in the future. P.S. May be I was in the process of brushing up my fundamentals in probability , this course didn't seem to be rushed and parochial as mentioned in other reviews.
Date published: 2020-04-11
Rated 5 out of 5 by from Very good. I really enjoyed this course and learnt (and re-learnt) a lot from it. Watching it through a second time made me appreciate it even more. One thing I would mention is that Professor Starbird doesn't read from an autocue (as most of the others do) and so it truly is like attending a lecture in the flesh. That means there are more pauses, and sentences chopped off and re-started, than if he was just reading from a script. This suits Professor Starbird's friendly and informal style, and it didn't bother me at all - indeed quite the contrary. However, if you like everything read faultlessly from a script then you might sometimes get frustrated.
Date published: 2019-10-10
Rated 5 out of 5 by from What are the odds? Very interesting. In Dr Starbird opening remarks about possibilities. He said one might wonder about the possibility of having a successful eye surgery. I had just had eye surgery and had got this DVD to keep my mind occupied while I recover. Is it just a coincidence or a good probability that someone who ha eye surgery or is about to have it would watch this DVD? Did he do any research on this possibility? If so, what were the odds?
Date published: 2019-05-30
Rated 5 out of 5 by from 1st Rate Course! Professor Starbird is a real pleasure to listen to. He fully understands the material and shows passion for his work. I really re-learned a lot of what I was previously taught. Hands down, this course is superior to any YouTube video on the subject.
Date published: 2018-04-28
Rated 5 out of 5 by from What Are the Chances? Probability Made Clear Professor Starbird's presentation includes surprising and nonintuitive results and thereby has the desirable quality of stimulating the student to delve more deeply into the subject.
Date published: 2017-12-27
Rated 5 out of 5 by from Great examples Happy to have bought this course.Good lectures and great examples are given by an excellent teacher.
Date published: 2017-07-01
Rated 3 out of 5 by from Not what I was hoping for The course is a general overview of what I would term the philosophy of probability. While there are entertaining anecdotal examples, do not expect to learn how to approach and solve probability problems. I thought that the lesson in which he discussed probability of rainfall to be a total waste of my time....sorry for being so harsh. I also would comment that watching these lectures illustrated one of the big drawbacks to this learning approach: the inability to ask questions to clarify issues. There were at least two specific cases where I would have like to ask a question where I believe the answer would have helped my understanding. Would I recommend this course? Yes, for people who have never been exposed to probability.
Date published: 2017-06-23
Rated 2 out of 5 by from A fair but not great introduction to probability I was hoping this course to be more in depth on the topic but was disappointed. I understand that a course of this length isn't really going to get into the math required, but I felt there were way too many things that were glossed over in the course. I did like the explanations of some things but felt that it was far too cursory for my liking.
Date published: 2017-03-31
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