Meta·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Meta data scientist interview with a probability/statistics question that felt more like a grad school exam than a product interview. One question, clean setup, but you need to actually know your Bayes.

Questions Asked (1)

Given a known fraud rate, a true-positive rate, and a false-positive rate for a flagging system, use Bayes' theorem to calculate the probability that a flagged account is actually fraudulent.

Product Analytics & MetricsAlgorithms & Data Structures

Author's notes

I knew the formula but fumbled the plug-in step because I mixed up which rate went where.

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AI HintsAI Generated

Suggested Approach

Start by clearly defining the events and given probabilities: base fraud rate (prior), true positive rate (sensitivity), and false positive rate. Then apply Bayes' theorem to compute the posterior probability that an account is fraudulent given it was flagged, and finally interpret the result in the context of the business problem.

Pro tip: Emphasize that the base rate (fraud prevalence) heavily influences the posterior, and discuss how even a highly accurate test can yield many false positives when fraud is rare. This shows you understand the practical implications of Bayes' theorem in real-world settings.

1. Define the events and probabilities

Let F be the event that an account is fraudulent, and + be the event that it is flagged. Write down the given probabilities: P(F) = fraud rate, P(+|F) = true positive rate, P(+|¬F) = false positive rate.

2. State Bayes' theorem

Recall Bayes' theorem: P(F|+) = P(+|F) * P(F) / P(+). Explain that P(+) is the total probability of being flagged, which can be computed using the law of total probability.

3. Compute the denominator

Calculate P(+) = P(+|F) * P(F) + P(+|¬F) * P(¬F), where P(¬F) = 1 - P(F). This accounts for both true positives and false positives.

4. Calculate the posterior probability

Plug the values into Bayes' theorem to find P(F|+), the probability that a flagged account is actually fraudulent.

5. Interpret the result

Discuss what the computed probability means for the business: e.g., if the probability is low, many flagged accounts may be false positives, leading to potential customer friction. Suggest ways to improve the system, such as adjusting thresholds or gathering more evidence.

Key Points to Mention

Bayes' theorem formula and its components (prior, likelihood, evidence, posterior).
The importance of the base rate (fraud prevalence) in determining the posterior probability.
The law of total probability to compute the denominator P(+).
The distinction between true positive rate (sensitivity) and false positive rate (1 - specificity).
Practical implications: high false positive rate can lead to many false alarms when fraud is rare.
Potential next steps: cost-benefit analysis, threshold tuning, or combining multiple signals.

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