Apply Bayes' rule to compute posterior
Company: Roblox
Role: Data Scientist
Category: Statistics & Math
Difficulty: hard
Interview Round: Take-home Project
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.
Quick Answer: 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.