What Are the Chances? Probability Made Clear
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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 underst& the r&om 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 r&om schedule.
In 12 stimulating half-hour lectures, you will explore the fundamental concepts & 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, & 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 & Myron Scholes, found a method to quantify those risks & 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 & 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 r&om event. In Lecture 2, you probe the nature of r&omness, which is famously symbolized by monkeys r&omly hitting typewriter keys & 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 r&om 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 & 6 show that r&omness & probability are central components of modern scientific descriptions of the world in physics & biology. Lecture 7 looks into the world of finance, particularly probabilistic models of stock & option behavior. Lecture 8 examines unusual applications, including game theory, which is the study of strategic decision-making in games, wars, business, & other areas. Then in Lecture 9 you consider two famous probability puzzles guaranteed to cause a stir: the birthday problem & the Let's Make a Deal® Monty Hall question.
Finally, Lectures 10-12 cover increasingly sophisticated & 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, & 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) & 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 & probability, including:
Gambler's ruin: A r&om walk is a sequence of steps in which the direction of each step is taken at r&om. In gambling, the phenomenon assures that a bettor who repeatedly plays the same game with even odds will eventually-& 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 & 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: R&omness plays a valuable role in reinforcing animal behavior. Changing the reinforcement in an unpredictable, r&om 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 & 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 & probabilities, then orders tests, & then refines the diagnosis based on the test results & 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.
R&omness 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 r&omness. It is a powerful tool for dispelling illusions & uncertainty to help us underst& the true odds when we roll the dice in the game of life.
1 Our R&om World-Probability Defined
2 The Nature of R&omness
3 Expected Value-You Can Bet on It
4 R&om Thoughts on R&om Walks
5 Probability Phenomena of Physics
6 Probability Is in Our Genes
7 Options & Our Financial Future
8 Probability Where We Don't Expect It
9 Probability Surprises
10 Conundrums of Conditional Probability
11 Believe It or Not-Bayesian Probability
12 Probability Everywhere