One of the most important topics in critical thinking is how to reason about chance and uncertainty. Human beings are prone to make mistakes in estimating the likelihood of events; in distinguishing meaningful correlations from mere coincidences; and in using probability information in drawing inferences and making decisions. Understanding some basic principles of reasoning with probabilities can help us be aware of these weaknesses in our reasoning.

Because probability is also a technical concept in mathematics and formal reasoning, it's easy to get bogged down in unnecessary technical details, which would not be helpful from a critical thinking perspective. My goal is not to make us experts in solving mathematical problems using probabilities.

My goal, rather,  is to help you develop "probability literacy" — a general sense of what probability is, the role it plays in our reasoning about the world, what mistakes we're prone to make, and what methods there may be to avoid those mistakes.

Probability is also deeply interesting from a philosophical perspective. It's not my primary focus in these lectures, but I do touch on some of these dimensions. I have found that the kind of probability literacy that I think is useful for critical thinking actually requires more background in the philosophy of probability than most mathematics students receive.

Thus, this material is divided into three parts.

Part 1: What is Probability? A gentle introduction to the philosophy of probability.

Part 2: The Logic of Probability. An introduction to the basic mathematical rules that govern correct reasoning with probabilities.

Part 3: Probability Fallacies. An introduction to errors that we're prone to make when reasoning about certain topics, e.g. coincidences, randomness, looking for causal explanations of probabilistic patterns, etc. 

This last section is incomplete, but there is still plenty here to chew on. My original outline had additional topics planned, but circumstances prevented me from completing them. I look forward to finishing this work at some point in the future.