In the full lesson
- Bayes' Theorem (formula)
- Medical Test Example (example)
- Base Rate Neglect (tip)
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Module 2 · Probability Foundations · Topic 8
Bayes' Theorem
Intuition. Bayes’ theorem lets you reverse conditional probabilities. If you know P(B | A) and want P(A | B), Bayes’ theorem connects them using the prior probability P(A) and the total probability P(B).
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Key formulas
From the Probability Foundations formula sheet
- Conditional Probability:
P(A | B) = P(A and B) / P(B)- Probability of A after restricting attention to cases where B occurred. - Bayes' Theorem:
P(A | B) = P(B | A)P(A) / P(B)- Updates a prior probability after observing evidence.
Related glossary terms
- Independence: Two events are independent when one occurring does not change the probability of the other. Example: Two separate fair coin flips are independent.
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