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This is a medium difficulty Machine Learning 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.

Build a Bayes classifier for reviewer types

Last updated: Mar 29, 2026

Quick Overview

This question evaluates Bayesian inference skills, including posterior updating under conditional independence, likelihood modeling for categorical observations, and application of Bayes decision rules with associated false-positive and false-negative rate calculations.

Bayesian Reviewer-Type Inference

Setup

There are two reviewer types:

Lazy (prior probability 0.20): always gives a "Good" review.
Careful (prior probability 0.80): independently gives "Good" with probability 0.60 and "Bad" with probability 0.40 on each item.

Assume conditional independence of reviews given the reviewer type.

Tasks

(a) Compute the marginal probability P(Review = Good).

(b) Given a reviewer produces 3 consecutive "Good" reviews and no "Bad", compute the posterior P(Lazy | 3 Good).

(d) Consider a Bayes decision rule that labels a reviewer as Lazy when the posterior exceeds 0.5. With b = 0, find the smallest g that triggers a Lazy label.

(e) If each reviewer is observed for exactly N reviews, express the false-positive and false-negative rates of this rule in terms of N.

Solution

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