Probability and Its Applications

Course Description

Don’t let them fool you! You hear people talking about probabilities all the time. 80% chance of rain? Well, what does that even mean? If a medical test gives the correct answer with 99% probability, does a positive test result mean you have a 99% chance of being sick? It does not. And when you hang out with your friends playing poker, wouldn’t you like to know the odds of winning with your hand before you go “all in”?

This is an introductory course in probability in which we study the basic concepts of probability and apply them to a wide range of real life problems. The course starts with some set theory (using Venn diagrams) and introduces basic counting. Counting helps answer simple questions such as: “Is Warren Buffet crazy? Or why does Buffet offer $1,000,000,000 for the correct March Madness bracket?” Then, we discuss concepts such as conditional probabilities, which will not only help your poker game, but which will also help you understand “false positives” of medical tests. If the pregnancy test is positive, how likely are you to be pregnant? Towards the end of the course, we introduce the concept of random variables and discuss some common probability distributions. This allows us to model many interesting real life situations. For example, call centers have an economic interest in modeling the waiting time until the next call. Accurate modeling allows them to balance operational cost, on the one hand, and customer satisfaction, on the other hand.

The goal of this course is to provide an intuitive understanding of probability. At the end of the course, you will be able to use the acquired skills and tools to solve problems and answer questions you encounter not only in school but also outside the classroom. Beyond that, a good understanding of probability is crucial because it is the foundation of statistics, which itself is becoming more and more important. The increasing amount of available information in the digital age is only waiting to be analyzed, and we should have more than just one Nate Silver, an American statistician, to do it. This course will lay the foundation in probability, which will allow you to take college-level statistics in the future, and maybe one day, you’ll be the one analyzing the data.

Prerequisites: Some knowledge of calculus is useful, but we introduce all necessary concepts as we go along.