Compute Bayes probability for fake accounts

Q: Compute Bayes probability for fake accounts

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.

Q: How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

Question

Loading...

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 $p, t, f, n$ .

Compute Bayes probability for fake accounts

Quick Overview

Solution

Comments (0)