Probability-The Engine of Inference

Dive into the world of probability and statistics in this dynamic course that explores the mathematical foundations behind decision-making under uncertainty. Beginning with the basics, we define probability as a measure of likelihood and its relationship to statistics. The course delves into key concepts like inductive reasoning, where generalizations are made from specific data points, and introduces probability as the driving force behind statistical inferences.

Through engaging with real-world examples and thought experiments, students will uncover how our intuition can mislead us in situations involving randomness and learn the significance of experiments and trials in estimating probabilities. The course also introduces Pascal’s Wager, using it as a springboard to explore expected value, and guides students through concepts such as complementary, independent, and mutually exclusive events.

A major focus is placed on understanding sample spaces and event probabilities to predict outcomes, and the role of the expected value in evaluating risks. Finally, the course explores the central limit theorem, showing why larger sample sizes yield more reliable results in both theory and practice. By the end of the course, students will be equipped with the tools and confidence to apply probabilistic thinking and statistical analysis to complex, real-life problems, offering a fresh perspective on how numbers drive the future. This course is ideal for those seeking to understand how probability informs decisions in everything from games of chance to critical life choices.