Apply Bayes' rule to compute posterior

Q: Apply Bayes' rule to compute posterior

Evaluates understanding of Bayes’ rule and basic probability concepts—specifically computing a posterior probability P(A|B) and the marginal likelihood P(B) from a prior and likelihoods—in the Statistics & Math domain at a foundational-to-intermediate abstraction level.

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Question

A binary event $A$ (e.g., “user is a payer” or “patient has a disease”) has prior probability $P(A)$ .

You observe evidence $B$ (e.g., a model predicts positive, or a test result is positive) with known likelihoods:

$P(B\mid A)$
$P(B\mid \neg A)$

Task:

Use Bayes’ rule to compute the posterior probability $P(A\mid B)$ .
Show how to compute $P(B)$ from the given quantities.

Optionally, illustrate with a numeric example to verify the formula.

Apply Bayes' rule to compute posterior

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Solution

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