Compute Bayes probability for fake accounts
Company: Meta
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Onsite
A platform is trying to detect **fake accounts**.
Assume:
- Base rate of fake accounts is \(P(F)=p\).
- A detection system flags an account as suspicious \((+ )\).
- True positive rate (sensitivity): \(P(+\mid F)=t\).
- False positive rate: \(P(+\mid \neg F)=f\).
**Part A (Bayes):** Given an account is flagged, compute \(P(F\mid +)\).
**Part B ("at least once" probability):** If you review \(n\) independently sampled accounts from the platform, what is the probability you see **at least one fake account**?
**Part C (combined):** If you review \(n\) independently flagged accounts, what is the probability **at least one of them is truly fake**? Express your answer in terms of \(p, t, f, n\).
Quick Answer: This question evaluates Bayesian reasoning and probabilistic modeling skills, including conditional probability, base-rate effects, detector characteristics like sensitivity and false positive rates, and calculations for "at least one" events.