Meta·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Meta data scientist interview with a probability question that sounds deceptively simple until you actually try to set up the math under pressure.

Questions Asked (1)

95% of accounts are real and 5% are fake. Fake accounts send friend requests at 10 times the rate of real accounts. If you receive a friend request, what is the probability it came from a fake account?

Product Analytics & MetricsRoot Cause Analysis

Author's notes

I knew it was a Bayes problem the second I heard it but still fumbled the setup.

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AI HintsAI Generated

Suggested Approach

Recognize this as a Bayes' theorem problem and set up the calculation using the given base rates and likelihoods. Assume a concrete number of accounts (e.g., 10,000) to compute expected friend requests from real and fake accounts, then find the posterior probability. Clearly state the assumptions and walk through the arithmetic.

Pro tip: Always sanity-check your result: since fake accounts send 10x more requests, the probability should be higher than the base rate of 5%, but not overwhelmingly so unless the rate difference is extreme. Also, mention that in practice you'd validate these rates with A/B tests or historical data.

1. Define the events and known probabilities

Let F be the event that an account is fake, R be real. Given P(F)=0.05, P(R)=0.95. Let the friend request rate for real accounts be r, so for fake accounts it's 10r.

2. Compute the probability of receiving a friend request

Using the law of total probability: P(Request) = P(Request|F)P(F) + P(Request|R)P(R) = 10r * 0.05 + r * 0.95 = 0.5r + 0.95r = 1.45r.

3. Apply Bayes' theorem to find P(F|Request)

P(F|Request) = P(Request|F)P(F) / P(Request) = (10r * 0.05) / (1.45r) = 0.5 / 1.45 ≈ 0.3448 or 34.5%.

4. Interpret the result and discuss implications

Explain that despite only 5% of accounts being fake, they account for about 34.5% of friend requests due to their higher activity. This highlights the importance of adjusting for activity bias in product analytics.

Key Points to Mention

Bayes' theorem and conditional probability
Base rate fallacy and the importance of prior probabilities
Law of total probability
Assumption of equal exposure or opportunity to send requests
Practical implications for spam detection and user safety
Sensitivity analysis: how the result changes if the rate multiplier or base rate varies

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