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Apply Bayes' rule to compute posterior

RobloxData Scientist · Online Assessment
HardData ScientistOnline AssessmentStatistics & Math

Last updated

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.

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:

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

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