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.

What difficulty level is this interview question?

This is a medium difficulty Statistics & Math question, commonly asked during Onsite rounds at Meta.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Meta during technical interviews.

Compute posterior and event counts in fraud screen

Quick Overview

This question evaluates a candidate's competence in probability and statistical inference, covering binomial probability calculations, Bayes' theorem for posterior probability, rare-event base-rate reasoning, and modeling of correlated binary signals in a fraud-screening context.

Fake-Account Screening with Threshold on 5 Signals

You are designing a rule-based screener that flags an account if at least k of 5 binary signals fire. Signals behave differently for fake vs. authentic accounts:

For fake accounts, each signal fires with probability p_f = 0.8.
For authentic accounts, each signal fires with probability p_a = 0.05.
Signals are independent within an account unless otherwise stated.

Let S be the number of signals that fire for an account (S ~ Binomial(n=5, p) under independence). An account is flagged if S ≥ k.

Tasks (a) For k = 2, compute P(flagged | fake) and P(flagged | authentic) using the binomial distribution.

(b) Assume a base rate P(fake) = 1.5%. Compute P(fake | flagged) via Bayes' theorem, and the expected number of flagged accounts in a day with 5,000,000 accounts scanned. Is a manual review queue of 80,000 per day sufficient?

(c) Find the smallest k such that expected flagged volume fits within 80,000 ± 5% (i.e., 76,000–84,000 per day) while maximizing P(fake | flagged). Show work and justify the precision–recall trade-off.

(d) If signals are not independent and have equal within-class pairwise correlation ρ = 0.2, explain how your answers and assumptions change. Provide a reasonable way to model this dependence and illustrate its impact on volume and precision.

Quick Overview

Fake-Account Screening with Threshold on 5 Signals

You are designing a rule-based screener that flags an account if at least k of 5 binary signals fire. Signals behave differently for fake vs. authentic accounts:

For fake accounts, each signal fires with probability p_f = 0.8.

For authentic accounts, each signal fires with probability p_a = 0.05.

Signals are independent within an account unless otherwise stated.

Let S be the number of signals that fire for an account (S ~ Binomial(n=5, p) under independence). An account is flagged if S ≥ k.

Tasks (a) For k = 2, compute P(flagged | fake) and P(flagged | authentic) using the binomial distribution.

Compute posterior and event counts in fraud screen

Quick Overview

Fake-Account Screening with Threshold on 5 Signals

Solution

Submit Your Answer to Earn 20XP

Compute posterior and event counts in fraud screen

Quick Overview

Fake-Account Screening with Threshold on 5 Signals

Solution

Submit Your Answer to Earn 20XP