Great Courses Plus – What Are The Chances – Probability Made Clear

These are just a few of the many possibilities that you’ll explore when investigating probability as a reasoning instrument:
When was the last common ancestor of all humankind?
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Great Courses Plus – What Are The Chances – Probability Made Clear

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 Because of the high likelihood that a bus stop’s waiting time will be longer than average, if they have a random schedule, it is likely that there will be a longer wait.

 In 12 stimulating half-Hour-long lectures on probability will help you understand the basics and discover some of the most fascinating applications.

 High Probability This Course Will Be A Hit

 Professor Michael Starbird knows how to make numbers live beyond non-Mathematicians love to find interesting, practical, and entertaining examples. Here are some examples that you can use in your exploration of probability as an reasoning tool.

• When was the last common ancestor of all humankind? Scientists have traced our lineage back to a female ancestor that lived around 150,000 years ago, using probabilistic methods.
• What should you pay to get a stock option? Options trading was considered gambling until 1970 when Fischer Black and Myron Schles created a way to quantify these risks and create a rational pricing model.
• What What do you do when third down is given with long yardage? If you have many yards to go, the obvious play is to pass. Naturally, the other team also knows this. Probability Game theory and game theory will help you to decide when to run with a ball to keep your opponent guessing.

What You will learn

 The Course begins literally with a roll on the dice. Professor Starbird shows that games of chance are a great way to illustrate basic principles of probability. He also explains the importance of counting all possible outcomes for any random event. Lecture 2 explores the nature of randomness. This is best illustrated by monkeys randomly hitting keys on typewriters and creating random outcomes. Hamlet. Lecture 3 explores the concept of expected values, which is the average net gain or loss from performing an experiment or playing the same game multiple times. Then, in Lecture 4, you will explore the simple but mathematically sound idea of random walk. While it might seem like an inexplicable way to get nowhere, it has many important applications in many fields.

 This introduction will provide a foundation for understanding the concepts of probability and allow you to explore the many applications. Lectures 5-6 show that randomness is a key component of modern scientific descriptions in biology and physics of the world. Lecture 7 focuses on finance, specifically probabilistic models for stock and option behavior. Lecture 8 covers unusual applications, such as game theory, which studies strategic decision making.-Making in games, wars and business. Next, Lecture 9 will discuss two famous probability puzzles that are guaranteed to make 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 Probability paradoxes are the end of course

 Take the Weather Forecasting Challenge

 Weather reports are a familiar experience of probability. They include predictions such as “There is a 30 percent chance of rain tomorrow.” But what does it mean? What Do You think? Pick one:

• (a) Rain will fall 30 percent of each day
• (b) Rain is possible at a certain point in the forecast area.
• (c) The forecast area is at 30 percent risk of rain during the day.
• (d) Rain will fall on 30% of the area forecast, but not 70%.
• (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 (e) is the correct answer and not any of the other options. He also explains why the National Weather Service’s official definition is incorrect.

 He even believes that in five years, the official definition of what he means will change as someone from the National Weather Service is going to give him this lecture!

 People play games

 The At the dice table, formal study of probability began. Gambling provides many examples of how probability and chance work, 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. Although the game may seem simple and profitable to the gambler, its expected value is incalculable! It is a game that no one would ever pay a lot to play. Why not?
• Gambler’s addiction: Randomness plays a valuable role in reinforcing animal behavior. Behaviors that are sustained for long periods of time even without rewards can be achieved by changing the reinforcement in an unpredictable and random manner. This observation can be applied to humans and may explain compulsive gambling.

 Probability The Rescue

 Thomas Bayes (18th century Presbyterian minister and mathematician) developed one approach to probability. It interprets probability as a function of degrees of belief. The calculation of probability is modified to account for new information as it becomes available. The Bayesian theory reflects the reality of how we adjust our confidence in knowledge as we acquire evidence.

 The A world of fluctuating probability, constantly adjusted as new evidence is discovered, captures how the world works in areas like medicine. Here, a doctor makes a preliminary diagnose based on symptoms, probabilities and orders tests. Then, the physician refines the diagnosis based the test results and new probabilities.

 This is how you work as a juror. The defendant is likely to be guilty or innocent at the beginning. As evidence builds, you adjust the relative probabilities that you assign to each verdict. Although you may not be able to do a formal calculation your informal process is Bayesian.

 Randomness surrounds us all. “Many or most parts of our lives involve situations where we don’t know what’s going to happen,”Professor Starbird says: Probability It comes in handy to explain what to expect from randomness. It’s a powerful tool to dispel illusions and uncertainty, helping us understand the true odds of winning when we roll the dice in life’s game of chance.