Compute posterior fake probability using Bayes' rule
Company: Meta
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
A platform runs an automated detector to flag fake accounts.
- Prior probability an account is fake: \(P(F)=0.02\).
- True positive rate (sensitivity): \(P(\text{Flag}\mid F)=0.90\).
- False positive rate: \(P(\text{Flag}\mid\neg F)=0.05\).
If an account is flagged, what is the probability it is actually fake, \(P(F\mid \text{Flag})\)? Show your calculation.
Overview: The problem evaluates understanding of Bayes' rule and conditional probability within the Statistics & Math domain for a Data Scientist role, at an introductory applied probability/interpretation level.