On this page, we discuss Bayes’ Rule for conditional probabilities.

Basic learning objectives

These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.

  • Use Bayes’ Rule to calculate a conditional probability by partitioning a sample space into two disjoint subsets.

Advanced learning objectives

In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:

  • Use Bayes’ Rule to do more general conditional probability calculations by partitioning a sample space into any number of disjoint subsets.

  • Use Bayes’ Rule in the context of a tree diagram.

  • Understand the base rate fallacy, prior probability, and posterior probability.

To prepare for class

  • Watch the following video (by Kevin deLaplante) which discusses a slight reinterpretation of the formula for a conditional probability, called Bayes’ Rule:

  • Watch the following video (by Art of the Problem) which discusses the relationship between tree diagrams and Bayes’ Rule:

After class

  • Watch the following video (by 3Blue1Brown) which introduces a way of visualizing Bayes’ Rule and discusses its implications:

  • Watch the following video (by Evan Wilhelms of the channel Deciderata) which gives more examples of the Base Rate Fallacy:


Brendan Cordy Avatar Brendan Cordy
Gabriel Indurskis Avatar Gabriel Indurskis






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