Bayes' Theorem and Law of Total Probability
Free SOA Exam P (Probability) lesson in General Probability. 21 min read, ~3,118 words.
Law of total probability:, this is the Bayes denominator. Bayes' theorem:, reverses conditioning direction. Posterior odds = likelihood ratio prior odds. Positive predictive value depends heavily on prevalence: rare disease + good test can have low PPV. Sequential updating: each posterior becomes the next prior.
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- Content
- Example 1
- Example 2
- Example 3
- Example 4
- Example 5
- Example 6
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Learning objectives
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