Roblox·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Got a Bayes' rule question for a Data Scientist role at Roblox, pretty much a classic probability derivation with a numeric sanity check tacked on. Nothing too wild but you do need to actually know the math cold.

Questions Asked (1)

Given a binary event with a known prior probability, and observed evidence with known conditional likelihoods, derive the posterior probability using Bayes' rule. Also show how to compute the marginal probability of the evidence from the given quantities, and optionally walk through a numeric example.

Product Analytics & MetricsAlgorithms & Data Structures

Author's notes

This is one of those questions where you either know the formula or you're staring at the whiteboard hoping muscle memory kicks in.

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AI HintsAI Generated

Suggested Approach

Start by clearly defining the events and given probabilities: prior P(H), likelihoods P(E|H) and P(E|¬H). Then apply Bayes' rule to compute the posterior P(H|E) and show the marginal probability P(E) as the denominator. Optionally, illustrate with a concrete numeric example to reinforce understanding.

Pro tip: Relate the derivation to a real-world scenario at Roblox, such as detecting bot accounts or predicting user churn, to demonstrate practical application and business impact.

1. Define events and probabilities

Clearly state the hypothesis H and evidence E, and list the known prior P(H) and conditional likelihoods P(E|H) and P(E|¬H).

2. State Bayes' rule

Write the formula: P(H|E) = P(E|H) * P(H) / P(E), and explain each term.

3. Compute marginal probability of evidence

Calculate P(E) using the law of total probability: P(E) = P(E|H) * P(H) + P(E|¬H) * P(¬H), where P(¬H) = 1 - P(H).

4. Calculate posterior probability

Substitute the values into Bayes' rule to find P(H|E).

5. Optional numeric example

Plug in specific numbers (e.g., P(H)=0.01, P(E|H)=0.9, P(E|¬H)=0.05) and compute the posterior to illustrate the process.

Key Points to Mention

Bayes' rule formula and its components
Law of total probability for marginal P(E)
Difference between prior and posterior probabilities
Importance of conditional independence assumptions (if applicable)
Base rate fallacy and its implications
Practical applications in data science (e.g., A/B testing, spam filtering, anomaly detection)

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.