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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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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Reviews

What Are the Chances? Probability Made Clear is rated 3.6 out of 5 by 74.
Rated 3 out of 5 by from Examples Needed While I enjoyed the professor's presentation of the world of probability, I would have appreciated some application of the formulas of probability. I purchased this course in hopes of better understanding how to use probability formulas to arrive at answers. My goal is to become a teacher of mathematics but I am having trouble with figuring the probability of an event. I did enjoy learning about the different types of probability and where they occur and would recommend it to a friend who was totally clueless to the world of probability.
Date published: 2011-07-17
Rated 4 out of 5 by from GOOD FOR BEGINNERS This course is good for beginners with little knowledge of probability. In the 12 lectures, Professor Starbird entices us to think more clearly about how probability impacts much of what we think and do. I appreciated his illustrations that initially appear counter intuitive, but which he guides us to rethink with simplicity.
Date published: 2011-07-10
Rated 4 out of 5 by from Conceptual Focus... If you want a good understanding of what probability is meant to measure, this is a good course. I enjoyed the applications on weather, genetics and finance and the lectures on Bayesian probs. My only dissapointment was the final lecture where Prof. Starbird could have done another example of two, rather than spend 15 minutes summarizing the course. Overall, a nice survey of what probability will and will not tell you.
Date published: 2011-06-06
Rated 5 out of 5 by from This course is actually fun [DVD] Probability is indirectly related to my work as a trainer of statistics software. Most of the TTC courses I have watched are as different from work as I can find. So, I got this one on a lark, but very much enjoyed it. Prof. Starbird is wonderful lecturer. He has style that manages to be both formal and informal, a little folksy, while still rich in content. Any series of lectures on probability will have dice, roulette wheels, and colored balls. These lectures have plenty of all three, and they are used to good effect. I never felt that the lectures were ONLY about these things - a flaw commonly found in lectures on this subject. He struck just he right balance between carefully chosen, easy to grasp, abstract examples, and down to earth practical examples. Real world examples, unfortunately, are often more complicated than rolling dice. As a result, Prof. Starbird often starts with playing cards, but then always moves on to something like the financial markets or the weather service’s definition risk of precipitation. I was especially pleased with the discussion of the fair pricing of stock options - a concept so seemingly complicated that I wondered how he could do it. Also, the final three lectures on Bayesian statistics were the clearest I have encountered. His use of the “Monty Hall” problem was not only fun, it was clearly explained, serving not only to entertain, but also to tie together concepts from earlier lectures. I was impressed by the amount that I learned in this course. I wondered if 12 lectures would be enough. I feel it was. My fear that it would not be enough stemmed from being exposed to so many poor lectures on this subject. Taught well, a lot can be covered, enough ultimately to be a good introduction.
Date published: 2011-05-10
Rated 3 out of 5 by from Entertaining Survey Any 12 lecture course should be expected to be little more than a survey, especially if dealing with a complicated subject. This course is no exception. I can understand the frustration of some reviewers with this course but I suspect it depends on how much you already have studied probabilities and how much you expect to know after this short course. If you view it as a survey, or "tasting" course and you are not well versed in probabilities you will get a great deal out of this course and it may help you to decide if you might want to know more about the subject. Probabilities can often help us to make decisions when faced with randomness. It is a component of statistics and often has counter intuitive results. Applications from gambling to medicine to investments and many other aspects of life make knowing something about probabilities useful. There are some very entertaining aspects to the course including the surprising likelihood that in a class of 50 students two students will share the same birthday. Also how probability can be used to determine if a very large (e.g., 300 digit) number is a prime number, something that can be impossible to calculate otherwise. His analysis of whether a football team on offense facing third and long should pass or run (and on defense whether to prepare for pass or run) was fun example and for those of us who enjoy football the results likely fit our expectations. And these are only a few of many entertaining examples he uses. The weakest part of the course was dealing with finance as it was in my view far to simplistic both as regards stocks and options and for those who are not knowledgeable about investments it is likely to confuse more than help. The strongest part of the course was dealing with probabilities that are surprising and unexpected. The professor tends to stumble in his presentation and has to correct himself at times. I found it made him human in an area where most of us find ourselves overwhelmed at times! He is enthusiastic which helps in dealing with what can be a very dry subject matter. Unfortunately I could not give this course more than average marks, but that does not mean I thought it not worthwhile. For those who want a sampling of what probabilities are and where they may be useful the course has value.
Date published: 2011-03-10
Rated 5 out of 5 by from Basic stats made fun and interesting Basic stats presented in a very interesting and entertaining (yes, entertaining) manner. The prof does this by giving a lot non-intuitive examples that are conveyed with physical examples, instead of obtuse math. The prof is a very lively and engaging speaker.
Date published: 2011-02-11
Rated 3 out of 5 by from Very elementary course I was expecting to learn far more than what I got from this course. Though Mr. Starbird is very very good at presentation but he just go through an over view of probability, not a single lecture on how to attack on those so much hard problems of probability. Which is Little frustrating. It would be nice if we get a higher level course on this subject.
Date published: 2011-01-30
Rated 1 out of 5 by from I tried Michael Starbird is a talented mathematician and teacher but in this course it is nearly impossible to learn much of anything--and it is all worth learning. So, I am deeply frustrated and somewhat embarrassed at spending money on something that was so promising but so chattererly confusing. I cannot recommend this course, at all.
Date published: 2010-06-11
Rated 5 out of 5 by from What are the chances? Very enthusiastic and likeable instructor. Material is presented at a very reasonable pace for the student with some mathematical background. Some of the results are intriguing yet unexpected.
Date published: 2010-05-23
Rated 2 out of 5 by from bad choice I thought this was a mediocre course. I've taken other Teaching Company courses and was quite pleased with them. But I found the teacher tedious and the material not terribly effective. I was going to purchase the statistics course until I found out it is taught by the same teacher. Guess I'll have to look elsewhere.
Date published: 2010-04-23
Rated 2 out of 5 by from Not a college-level course I bought this course as part of a set with Prof. Starbird's statistics course. Unfortunately both courses try to teach math without using math. So far my impression is that The Teaching Company's high school math courses actually teach how to do the math, while their "college" courses try to avoid it. When I buy a math course, I want to learn actual math.
Date published: 2010-03-24
Rated 2 out of 5 by from Too Basic Having spent more than enough hours studying various forms of Mathematics, I was disappointed that a subject with so much potential for exploration was treated so blandly,in my opinion, this was high school stuff, granted I went to Catholic school, but I expect to be challenged by learning -- we figured the dice thing out shooting craps behind the church.
Date published: 2009-12-22
Rated 3 out of 5 by from An Easy Math Course I was expecting this to be a rather dull, math-formula heavy course which might require hiking boots in order to plod all the way through, but I was pleasantly surprised. If anything, this course was far too basic, and many of the points made by the professor to show how counter-intuitive probability can be, struck me as, well, just plain intuitive. In discussing the wide variety of interesting topics to which he applied the principles of probability, the professor seemed a bit less than well-organized, or perhaps he is simply not a particularly great speaker. In any case, the lectures were easy to understand and fun. The DVDs presented the math formulas on screen, which was helpful. I did notice a problem with the "Monty Hall" presentation, in which I am afraid, the intructor just dropped the ball. (Even I can easily prove that his claims regarding which door to pick were simply mistaken.) Many people may find this course to be enlightening and fun. As for me, I was shocked -- yes, shocked -- to find that there was gambling going on here! Or rather, I was surprised that the course was so easy that I zipped through lecture after lecture, without any difficulty. The longer course on Statistics may be more my speed (I don't want a "tough" course, but I do want to learn more). This was my first (and so far, only) TTC math course, but I think it is highly probable that this is among their easiest and most basic courses.
Date published: 2009-10-28
Rated 5 out of 5 by from A Fun Course I've enjoyed all of Professor Starbird's courses, and this was no exception. The topic is an interesting one, and the enthusiasm and sense of fun Professor Starbird brings to his teaching is a pleasure.
Date published: 2009-07-26
Rated 2 out of 5 by from Not a college-level course I set my expectations based on other courses by Prof Starbird from TTC, but this time I was deeply disappointed. The first three lectures, while very basic, offered promise. After that, the lectures were increasingly about pointing out to you that probability is involved in many areas of life, but the course content was more informative of the science (or finance) than providing any real insight beyond the fact that complex probabilistic models existed within these fields.
Date published: 2009-07-17
Rated 5 out of 5 by from Fun course! This was a fun course. Dr. Starbird is delightful and thorough in his explanations. He makes up stories and puts the concepts in real world use. We use probability all the time and most of the time aren't aware that we are. He draws in the listener with descriptions and scenarios that we can relate to but why anyone would bother to gamble is beyond me. Just write a check to charity and say you gambled. This course was an eye-opener in many respects. Watching this course instead of TV was a better use of time.
Date published: 2009-07-02
Rated 5 out of 5 by from Excellent Course I really enjoyed this course. It hit just the right combination of practical techniques and interesting observations about the areas of life that Probability plays a key role, e.g. genetics, finance, gambling and sock drawers! Michael Starbird, is an enthusiastic lecturer who delivers the material in a very interesting way. You can sense him willing you to comprehend what he says. Generally easy to follow (unless you are mathematically challenged), the explanations are quite comprehensive. I particularly liked the sections on conditional probability and Bayesian probability. On the negative side, I thought the lecture on Options was quite weak and the explanations of the two envelope paradox was confused and I still don't know why the expected value calculation answer is wrong ! Overall, very good and certainly worth 6 hours of your life. I will be watching his statistics course in the near future.
Date published: 2009-05-29
Rated 5 out of 5 by from A good Overview Prof Starbird is an excellent presenter, he gives a range of different problems with good visual aids to help understanding. I thought the explanations of Probability Walks, Gambler's ruin, Let's Make a Deal, the Birthday Problem and Game Theory were excellent. The Conditional Probability lectures need better examples. Also, I would have liked to have seen more links with Statistical Probability, but the course was good.
Date published: 2009-04-05
Rated 5 out of 5 by from I love this guy I am wrapping up my MS in Finance and I think Starbird is great. I've picked up a few new things listening to him, as well as tweaked my old way of viewing probability. I also appreciate his humility. It is clear that he has a true passion for the field. Lastly, if you purchase his statistics course, view the one on probability FIRST.
Date published: 2009-03-21
Rated 2 out of 5 by from Missed the Mark I failed to connect with this course. This was my first Teaching Company math course (the others have all been in the liberal arts) so perhaps it was just me, but I did not think the course lived up to its billing (the first time I can say that about any Teaching Company course I have taken). I found Professor Starbird hard to follow at times, felt he made certain leaps of logic, and did not find some of his conclusions to be particularly useful in the real world (in contrast to what I had anticipated from the course description). This is the first Teaching Company course I really struggled to complete.
Date published: 2009-01-25
Rated 5 out of 5 by from Excellent Discussion As with most TTC science and math products, this course gives you a "view from the top" of the breadth of the subject, and takes you up to, but NOT through, problem solving. Prof. Starbird does an excellent job of this, and takes you through many instances of day-to-day events which involve probability. Although he shows you how some problems are solved, this is not the emphasis. Although probability is mathematics, remarkably little math is used in this course, and even that is optional to understanding the topic. If you want to follow the math, all you need is high-school algebra. By not getting bogged down in detail, you are free to appreciate the impact of probability on everyday life. And I guarantee some of the examples Prof. Starbird provides are really going to surprise you. If you plan on going past this, possibly to a formal course in probability, the preparation in this course will make you more productive in that effort. Prof. Starbird is an excellent teacher, and I very much enjoyed this course.
Date published: 2009-01-04
Rated 4 out of 5 by from Not the ideal probability course I agree with "Alvi" that the treatment of the topics in the course was superficial, and that a more in depth course spanning a greater number of lectures would have been better. Moreover, in his haste to cover a lot of ground, the professor did not properly explain some of the background material required to make proper sense of his lectures on finance and biology. I have seen much better explanations of the Hardy-Weinberg equilibrium and genetic drift in basic biology textbooks. A simple thing he could have pointed out is that the Hardy-Weinberg equilibrium is theoretically possible only if the population size is infinite, and genetic drift is possible only when the population size is finite. Finite populations will never stay at the Hardy-Weinberg equilibrium and infinite populations (theoretically speaking) cannot have genetic drift. I don't have a background in finance at all and wasn't able to understand his explanations in the finance lecture. On the positive side, the purely mathematical parts of the course - the Monty Hall paradox, St. Petersburg paradox, the birthday problem, the gambler's ruin, etc were presented quite well.
Date published: 2008-12-30
Rated 4 out of 5 by from Not Bad, But Should Have Gone Deeper On the positive side, the course provides some interesting and useful information and, as usual, Starbird is a personable and effective lecturer. But I feel that the course represents something of a missed opportunity. In a course devoted entirely to the topic of probability, I think it would be reasonable to assume that most members of the audience would already be familiar with the basics of probability, and would therefore be looking for a fairly in-depth treatment covering the history, philosophical dimensions, mathematics, applications, and paradoxes of the concept. Instead, what we get is a somewhat superficial treatment of all of these areas, as though the lecturer is afraid we can't handle more, with the result that I was more tantalized than satisfied. I don't think the problem is that 12 lectures isn't enough, but rather that the course simply needs to be presented at a moderately more advanced level. I suppose I can still recommend the course to people who are interested in the topic and have limited background in it, so I guess 4 stars can be justified. But people looking for a deeper treatment of the topic may want to skip the course unless they don't mind reviewing material they're most already familiar with, just for fun.
Date published: 2008-12-25
Rated 5 out of 5 by from The video course serve to motivate you to look up the books in the reading lists to reinforce your video learnings. That's what a good teacher does - motivates you to learn more on your own.
Date published: 2008-10-17
Rated 5 out of 5 by from Mike Starbird is a great and fluent professor. He can even teach math ideas to people who didn't even go to high school.
Date published: 2008-10-17
Rated 5 out of 5 by from Prof. Starbird makes a potentially complex and boring subject light and intriguing. I like his use of demos, and his interaction with the audience in the opening view.
Date published: 2008-10-17
Rated 4 out of 5 by from Gave good understanding of course- a little light on the formulas.
Date published: 2008-10-17
Rated 4 out of 5 by from The course was more basic than expected. THe professor seemed at a loss for words more than often than he should have been & repeated some things too often, so i'm talking to screen to ok ok move on, otherwise examples worked well & content was very clear
Date published: 2008-10-17
Rated 3 out of 5 by from THe text was redundant. Wish I hadn't bought it
Date published: 2008-10-17
Rated 5 out of 5 by from DR STARBIRD PRESENTS DIFFICULT CONCEPTS WITH EXCEPTIONAL CLARITY. HE HOLDS HIS LISTENER'/VIEWERS' ATTENTION BY KEEPING THEM IN SUSPENSE! LIKE ALL GOOD LECTURERS , HE IS A GOOD ACTOR TOO.
Date published: 2008-10-17
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