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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What Are the Chances? Probability Made Clear is rated 3.7 out of 5 by 75.
Rated 1 out of 5 by from I really wanted to like this, but... I'm a long time customer and have bought and enjoyed dozens of TG courses. This is not one of them, unfortunately. The primary problem is its outdated format. This looks like one of the first courses TG made, because it is shot in front of a live audience without a teleprompter. Clear presentation is not the professor's strong suit, who fumfers throughout the entire presentation, with more "ums" than pedagogical content, it often seems. The use of graphics is poor and the live probabilistic demonstrations with dice use dice too small to be seen on a cell phone screen (as I said, this course is old). Perhaps the professor is very knowledgeable, but his un-prompted presentation was so poor I had to return the course. I am very interested in the subject matter, so I hope TGC re-records the course, or one similar, with an updated format (and a teleprompter).
Date published: 2016-10-24
Rated 4 out of 5 by from Randomness Everywhere Professor Starbird has a passion for math and his aim is to provide an overview of probability concepts to non-mathematicians. Professor Starbird has chosen many classic problems and applications from various fields to illustrate probability concepts. For me personally, I enjoyed lecture 5 where Professor Starbird discussed weather forecasting in detail, i.e., What does it mean if there is a 30% chance of rain tomorrow? Lecture 3 on Expected Value is important if you want to understand probabilities of playing games of chance. Lecture 10 (conditional probability) discuss an important probability concept that often trips up professional practitioners and statisticians alike. If you’ve ever struggled with understanding Bayesian probability, or tried to use the Bayes Rule formula, Professor Starbird provides an intuitive example in lecture 11. In my experience, if you’ve taken a probability course, then this course can add some conceptual understanding to the formula-based instruction you likely received. However, if you haven’t taken a probability course, you will gain a conceptual overview of probability, but will likely not be able to apply these methods without further training.
Date published: 2016-09-12
Rated 5 out of 5 by from Excellent Practical Information This course is very practical in making clear the issue of risk-reward which is such a part of everyday life. The lecturer is very dynamic and makes his points clear. I especially appreciate how he has used the power of the computer to analyze random events so thoroughly. As well as showing the math involved in computing the various probabilities he also gives clear explanations of the process. I very much enjoyed this course.
Date published: 2016-06-04
Rated 4 out of 5 by from Interesting course I learned a lot about probability through this course. Really enjoyed the lectures on using probability in real life situations. A few times I got confused tying to understand what the instructor was really saying about a topic.
Date published: 2016-02-06
Rated 2 out of 5 by from Important subject but not very well presented I was hoping for more from this course which does cover a very important subject. It's a reasonable general introduction for those not familiar at all with statistics. He does make a good case about how statistics and randomness are everywhere in our lives. I had hoped for more depth such as the bell curve, average vs. mean, variance, multi-modal statistic (at least a statement about the existence of populations/situation where these exist), large vs. small sample testing, etc. I do love the Great Courses because they don’t get bogged down in math drills so I'm not advocating for the standard university statistics course like I took some 40-years ago. I would like, however, a course that reviews the top-level concepts, applications and challenges involved with applying and interpreting statistics the right way and how statistics can be inadvertently and/or purposely manipulated. In this regard, this course fell far short of my objective.
Date published: 2015-10-30
Rated 1 out of 5 by from texas bloviator This guy probably could have made the material clear and accessible, but instead he chose to stand and talk with what might have been, to him, meaningful hand movements along the way. Lakes become rivers and then become lakes, again, not central to the argument but an indication of lack of focus. Examples are mostly not explained after being worked out, so that what might be helpful, a sound and clear working through of just exactly how this unanticipated outcome is in fact probable, just never happened. I cannot understand how this guy got highly rated, nor would I be interested in another course taught by him.
Date published: 2015-08-01
Rated 4 out of 5 by from Well Worth the Price This is not a course in statistics but a well presented introduction to real world random events and finite mathematics. True, Starbird does not mention permutations and combinations by name but gives examples of how they are used starting with the first lesson. If you find the subject fascinating (as I do) take a look at a couple of books by authors Leonard Mlodinow and Deborah J. Bennett.
Date published: 2015-06-19
Rated 5 out of 5 by from Great Course I thought this was a very good course. As a person who has not gone to university, I was glad to not be bogged down with a lot of math. The math was simple enough to follow in my head but it described the concepts well. I liked the professor and thought he showed genuine enjoyment in the topic, and his occasional stammering (which other commenters have pointed out) didn't bother me a bit.
Date published: 2015-06-16
Rated 4 out of 5 by from My review of "What are the Chances: Probability Made Clear" by Michael Starbird: Professor Starbird makes this course enjoyable and fun as he makes cases of flipping a coin or rolling a dice, as well as talking about the game show "Let's Make a Deal" hosted by Monty Hall.
Date published: 2015-05-23
Rated 4 out of 5 by from Probability is a difficult subject, and it would take a much longer course to begin to do it justice. I believe Dr. Starbird did a good introductory job. He had good examples of determining probabilities, and how one might go wrong at it. I'm not as happy with this course as with 'Thinking Like an Economist', but the subject matter is different enough to make a close comparison difficult.
Date published: 2015-03-02
Rated 5 out of 5 by from Terrific Communciator Professor Starbird takes a difficult topic for those of us who are not naturally numerate and are well beyond our university years and makes it exciting and relevant .
Date published: 2015-01-31
Rated 4 out of 5 by from What Are the Chances? Probability Made Clear Excellent detailed presentation on ones chances of making the correct decisions on everyday opportunities. If you want to obtain a better understanding on topics of interest to you, it would definitely be an absolute benefit to check out the offerings of The Great Courses, Each course is clearly presented by a master of the topic, is cost-effective and once obtained is always available for review and a more in-depth understanding of the subject.
Date published: 2015-01-27
Rated 1 out of 5 by from Old school style Worse buy, kick myself for not reading feedback b4 purchase. Does not mention combination or permutation when covering that topic. He is knowledgable, not an effective teacher. I learned more from Jason Gibson of MathTutorDVD.com. He is the best! I had subscribed for more that 3 years, still active. Highly recommend for this topic. I thought I would explore other lectures, am disappointed.
Date published: 2014-04-21
Rated 2 out of 5 by from Not Very Advanced I tutor high school and college students. I was looking for something that could help me better explain some of the formulas. Unfortunately, the material on these lectures is very basic and was not sophisicated enough for anything beyond the third week on a basic high school level stats class. If you just want to learn about stats, you might enjoy this. If you want to learn stats at a high school course level, you will need to find something more advanced.
Date published: 2014-04-15
Rated 5 out of 5 by from Clear presentation This is a well-organized course, presented with clear, understandable examples. It provides a good basis for the study of statistics, and highlights the idea that the reality of probability may be at odds with intuition or "common sense", providing an important critical thinking tool.
Date published: 2014-03-06
Rated 4 out of 5 by from Useful and revealing! I have truly been enjoying this video and may watch parts of it again to cement my understanding. You don't need to be a mathematician to understand it, and there are many real-life examples. I only have two minor gripes: 1, The speaker really needs to look at the camera. It's almost as if he is deliberately avoiding eye contact. I find this very distracting. 2. While there are visual aids and charts, they border on the bland and boring. Certainly, with today's technology, the visuals could have much more impact.
Date published: 2013-08-28
Rated 4 out of 5 by from as he said: more homework, please Overall an entertaining course with quite a few revelations. But ... Prof. Starbird said it: The TGC should "promote" more kind of homework! I totally agree as frontal presentation is one thing, but having to work on a probabilty problem oneself is different and for me probably more helpful. (It depends on the kind of explanation/solution.) Nevertheless a recommendable introduction which encouraged me to dig deeper .... (--->>> TGC ... part II ???).
Date published: 2013-06-12
Rated 3 out of 5 by from Not as Practical as I'd Hoped By the second lecture, this had become pretty much an armchair course-- Interesting in general terms, but not very helpful on the practical level. Professor Starbird's delivery, though fairly laid back, didn't come across as polished as I would have liked. A few key points became tangled and on occasion he suddenly stopped midstream and used a mulligan. My mixed metaphors aside, the best I can say is it was mediocre. I would have liked more "homework" with which to hone these techniques. I need repeated drill with pencil and paper in order to cement these algorhythms and techniques. Dr. Starbird also hurried througth a proof or two which I would have liked to have seen in more detail. I realize he does this sort of thing almost second nature, but it's been a while since I did rigorous proofs. Those rigorous proofs helped me take algorhythms from rote to a more solid foundation. All in all I enjoyed the course, just not quite as much as I'd hoped.
Date published: 2013-03-22
Rated 4 out of 5 by from Good, Solid, Fun Course This was a good course. It had been many years since I'd taken statistics and although probability is a bit different, this course brought many concepts back to mind. The variety of topics, from gambling to "Let's Make A Deal" was, I thought, excellent. I've seen other reviews in which the reviewers felt the course wasn't didactic enough, but frankly, this is exactly what I was looking for - a fun course with examples we can all understand. The professor was clearly knowledgeable and in my opinion presented most information coherently and often from several perspectives so as to make his point more clear. There was one (I couldn't find others) in which the conclusion didn't seem to quite match his description. I think I understand what he meant, but was confused ("Let's make a Deal" and the Cadillac being behind door #1 - I think he just said it poorly - I assume he meant the odds were 2/3, not "definitely behind that door). There were several times when I needed to "ask a question", and my guess is that others' would have the same concern - why, if one had (his example) 1,000,000 doors, and someone chose one, once 998,000 where opened with nothing behind them, you should switch doors due to overwhelming odds that you chose the wrong door. Don't the odds change as the range of correct doors is narrowing down? Wouldn't the odds be different is someone came along once 998,000 doors where open? And how can the odds be different for 2 different people? Having said that, it was fun, entertaining, somewhat insightful, and I'd recommend it to a friend.
Date published: 2013-01-26
Rated 3 out of 5 by from Disappointing Course From a Good Teacher I took this course because I had taken excellent courses from this teacher, because I needed a periodic review of the topic, and because of the relevance for this course for our lives (I am a doc and probability/statistics are perhaps the only advanced math courses I frequently use). If we don't know enough about prob/stats, the chances are higher we will make poor judgments about health literature, as well so many other areas in our lives. Alas, for those of us who do not intuitively think in a probabilistic or statistical fashion (and Prof Starbird points out that would be the vast majority), we need to periodically review the subject to maintain adequate proficiency. In the past, I've used textbooks (like the excellent Seeing Through Statistics or the good Schaum's Outline) but this time decided to try a visual method, so I bought this course. The "take-home lessons" from this course were conceptually good, and included just how frequently intuitive assessments seem to clash with probabilistic analysis (suggestion: when the two conflict, go with the analysis instead of the surface common-sense view), how we may gather useful information even when uncertainty and randomness are involved, and that certitude is more rare than we think (especially when we have a strong opinion). Unfortunately, the course took too a round-about route with too many detours on its way to giving these insights. For example, it seemed the lectures focused too much on examples from gambling and games of chance, rather than on examples from normal living. I'm not sure if the visual method is less effective than standard written textbooks, if you need to work with study problems to reinforce the methods (the course only had one), or if twelve lessons are just too few for this topic (perhaps, instead, I should ask "what is the probability of an effective lecture, given the nature of the topic, its presentation, the coursework involved, and the time available"), but I was just less than impressed with this particular class. I would give him a chance on other math classes, though, and indeed I am again enjoying his review course on calculus right now.
Date published: 2012-10-22
Rated 2 out of 5 by from Muddled The prof is obviously a very nice man and it pains me to write this, but it's time for him to retire. He blunders his way through this lecture, making numerous mistakes in every episode. Yes, he goes back and corrects himself, but that is not good teaching. Where he needs to be detailed, he skims. Where details are unnecessary, he supplies them. Was my appreciation for the material enhanced by watching this? Not a bit.
Date published: 2012-07-14
Rated 1 out of 5 by from Unstructured and not informative I have watched about a dozen courses before, but this one was truly disappointing. Prof. Starbird may be a distinguished teacher at university, but his presentation style is utterly unsuitable for DVD. He never looks at the camera and doesn't follow a script. He often repeats himself and his train of thought is incoherent and his language difficult to follow. To my dismay I discovered that I have another course of his in my collection, which I will try to return.
Date published: 2012-07-09
Rated 3 out of 5 by from Basic Material with Some Interesting Implications I would not let this “mathematics” course scare you away if numbers are not your forte. The mathematical concepts discussed in this 12-lecture course are fairly basic, closer to high school than college level, in difficulty. However, the implications of the basic concepts presented can be quite fascinating, and this is where the value of this course lies. If any of the following scenarios perplex you I suggest that you explore this course from Professor Starbird to investigate further. 1 – Roulette - About 61% of players will be ahead after placing 35 $10 bets in roulette despite a distinct advantage to the house in collecting, on average, 53 cents profit for each $10 bet placed. 2 – The Monty Hall/Let’s Make A Deal problem – Does it make any sense to switch from Door #1 to Door #3 after Monty has shown you that the new car is not behind Door #2?? 3 – A gambler with a fixed amount of money to wager will eventually lose it all even in a fair casino with no advantage to the house. The lecture on the random walk (#4) should be required viewing for all baseball writers and sportscasters who seem to have little conception of probability theory. They should be required to take some random walks through a 162 game season of an eventual pennant-winning team and see that both winning streaks and quite lengthy losing streaks can occur by chance. Then we would not have to listen to their musings about the disaster of a season ahead just because their team drops the opening three game series! I completed this course shortly after watching the course “Understanding Complexity” taught be Professor Page. Complexity theory asserts that randomness can be a product of complex systems. Professor Starbird did not provide any thoughts on just where “randomness” originates – in nature, in science, in financial circles, or elsewhere. He implies that it is just there. Perhaps a lecture on the origins of random phenomena and the relationship of randomness to complexity might be a better use of lecture 12 than simply a review of the important learning points of previous lectures. In addition, probability is closely tied to statistics, and this course seemed incomplete without some mention of basic statistical concepts. Lectures on statistics have been saved for inclusion in another Teaching Company course taught by Professor Starbird.
Date published: 2012-07-01
Rated 3 out of 5 by from Not Very Good I didnt like this. It seemed very shallow and elementary. Just not much here of any value.
Date published: 2012-06-05
Rated 3 out of 5 by from Good, but... I am still perplexed by the Monty Hall problem. Professor Starbird says that if the contestant chooses Door #2 and Monty Hall opens Door #3 to show a lousy prize, the contestant must change their choice to Door #1 "and they will definitely win the Cadillac." So he's saying then, that there is no chance that the car is behind Door #2. Why not?
Date published: 2012-03-09
Rated 4 out of 5 by from Less Math than Expected I had already taken a research methods class on stats, but the probability was only a footnote, so I was hoping this would at least provide with a foundation for further research. While the professor used excellent examples from meteorology for physics to sports for game theory, he seemed to neglect the math. The examples were interesting but i didn't see much math until game theory lecture with systems of equations.He does show data on a lecture dealing with fish ecosystems but I do not remember much explanation for the numbers. Many examples are also taken from gaming. The options lecture had almost no background provided and math is certainly needed for finance. I learned about some interesting problems like the birthday problem, but it felt more like story telling. I would recommend this to someone who does not want a mathematical intro to probability. On a positive note, I was almost never lost in his lectures, with the fish lecture being the only time. He makes great use of visuals, and I liked his intro to probability with the dice. Mathematically, the course failed in providing research, but it did succeed in introducing new concepts.
Date published: 2012-03-05
Rated 4 out of 5 by from Pretty much as advertised... This is an entry level course on probability. With just 6 hours of lecture time, it is reasonable to expect only an overview of this subject. Usually this subject is taught to college juniors and seniors, yet Dr. Starbird has done a good job making the course accessible to anyone with high school math. There are enough examples, and there is not too much math, formulas, etc. Dr. Starbird has a teaching style that may seem a bit slow or uncertain, but in fact he is enthusiastic and energetic, explaining the subject well with examples and humor. I'm sure his students at Texas appreciate him, given the list of teaching awards he has won. (But a word of advice to those students: Don't bet against Dr. Starbird's choice on some question of probability, not even a single dollar.) Some of the examples explained seem to defy common sense or intuition. But as Dr. Starbird expresses, that means that our common sense needs to be adjusted or better educated. And if Monty Hall gives you a chance to choose a different curtain from your initial choice... Well, I'll let Dr. Starbird explain that one to you.
Date published: 2012-02-03
Rated 1 out of 5 by from poorly taught The value being taught any math course is that it is so difficult to understand math concepts by simply teaching oneself. The good math teacher can simplify and illustrate concepts and inform...unfortunately, I didn't find Prof. Starbird's lectures informative-more confusing than helpful-and I have a Ph.D. in physical chemistry and have taken more than my share of advanced math courses and done exceptionally well. If nothing else, it made me appreciative of the math instructors I've had that have been able inform me...without them, I'd be as confused as I was watching Prof. Starbird's lectures. In summary, he just doesn't explain things well.
Date published: 2012-01-20
Rated 2 out of 5 by from Not for serious or even casual learning How can one explain a maths course without using maths? Buy it if you only want to view some social events through probability concepts for a change. This is also good for someone who has no prior knowiedge in the subject matter and is very interested to listen to some probability stories. For students who want to learn you will be disappointed.
Date published: 2011-12-22
Rated 4 out of 5 by from Lightweight A good course for beginners. A more indepth presentation would have been better. That being said, the course is still worth the time. DVD
Date published: 2011-11-03
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