What Are the Chances? Probability Made Clear

Overview

Explore the fundamental concepts and fascinating applications of probability in this fun and engaging course by an award-winning mathematician. Every time you buy a stock, play poker, or make plans based on a weather forecast, you are consigning your fate to probability. These 12 fascinating half-hour lectures help you understand the random factors that lurk behind almost everything.

Professor Michael Starbird of the University of Texas at Austin 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? How much should you pay for a stock option? What do you do on third down with long yardage?

After an introduction to the key concepts of probability, you will delve into the wealth of applications, from biology to physics to finance to war. Probability comes to the rescue to describe what we should expect from the randomness of life. Take hold of this powerful tool and you can dispel uncertainty and understand the true odds in the game of life.

Course Structure

01: 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.
Duration: 33 min

02: 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 is to be expected from randomness.
Duration: 31 min

03: 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.
Duration: 31 min

04: 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.
Duration: 31 min

05: 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”?
Duration: 31 min

06: 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.
Duration: 29 min

07: 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.
Duration: 31 min

08: 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.
Duration: 31 min

09: 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.
Duration: 31 min

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.
Duration: 30 min

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.
Duration: 30 min

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.
Duration: 32 min