Bayes’ Theorem

In this lesson of this conditional probability course, we’ll learn about Bayes’ theorem, which is a central topic in probability. In the last lesson on intermediate conditional probability, we continued learning about conditional probability and focused on subjects like the multiplication rule, the order of conditioning, and statistical independence.

In addition to learning how to calculate probabilities using Bayes’ theorem, you’ll take in in-depth look at how independence is different than exclusivity as well as how to calculate probabilities using the law of total probability. You will also learn how to calculate the prior probability as well as the posterior probability.

Even though there is no dataset in this lesson, you will still have the opportunity to complete exercises as you go through this lesson. By the end of this lesson, you will be able to feel completely confident with the calculating probabilities using the law of total probability as well at Bayes’ theore mand be well-equipped to better estimate probabilities.

As you work with through learning more of conditional probability, you’ll get to apply what you’ve learned from within your browser so that there’s no need to use your own machine to do the exercises. The R environment inside of this course includes answer checking so you can ensure that you’ve fully mastered each concept before learning the next concept.


  • Learn independence vs. exclusivity.
  • Learn the law of total probability.
  • Learn how to use Bayes’ Theorem.

Lesson Outline

  1. A Review on Mutual Exclusivity
  2. From Conditional to Marginal
  3. A General Formula
  4. Extending Our Formula
  5. The Law of Total Probability
  6. Bayes’ Theorem
  7. Prior and Posterior Probability
  8. Next Steps
  9. Takeaways

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