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Sig·Software Engineer·Technical Phone Screen·Junior

Junior
May 2026

Summary

Interviewed for a quant researcher role at SIG. One probability question, classic Bayesian setup. Pretty standard for this kind of shop but still easy to fumble if you rush it.

Questions Asked (1)

Q1

Factory A produces 40% red and 60% black widgets. Factory B produces 80% red and 20% black. A factory is chosen at random, then two widgets are drawn from it. Both come out black. What's the probability they came from Factory A?

A/B Testing & ExperimentationTechnical Trade-offs
Author's notes

Bayes all the way.

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AI HintsAI Generated

Suggested Approach

Recognize this as a Bayesian inference problem: you need P(Factory A | two black widgets). Use Bayes' theorem with the prior probability of choosing each factory (0.5) and the likelihood of drawing two black widgets from each factory (computed via the binomial distribution). Compute the posterior probability by multiplying prior and likelihood for each factory, then normalizing.

Pro tip: After computing the exact probability, mention that in an A/B testing context, this is analogous to updating your belief about which variant is better given observed data. Also, sanity-check the result: since Factory B has a lower probability of black widgets, observing two black widgets should decrease the probability it's Factory A, so the posterior should be less than 0.5.

1. Identify the goal and given probabilities

State that you need P(A | BB). Note the prior P(A)=0.5, P(B)=0.5, and the conditional probabilities of drawing a black widget from each factory: P(black|A)=0.6, P(black|B)=0.2.

2. Compute the likelihood of two black widgets for each factory

Assuming independent draws with replacement (or from a large population), calculate P(BB|A) = 0.6 * 0.6 = 0.36 and P(BB|B) = 0.2 * 0.2 = 0.04.

3. Apply Bayes' theorem

Compute the unnormalized posteriors: P(A)*P(BB|A) = 0.5 * 0.36 = 0.18 and P(B)*P(BB|B) = 0.5 * 0.04 = 0.02. Then normalize: P(A|BB) = 0.18 / (0.18 + 0.02) = 0.9.

4. Interpret the result and connect to the role

Explain that there is a 90% chance the widgets came from Factory A. Relate this to A/B testing: updating prior beliefs with observed data to make decisions.

Key Points to Mention

  • Bayes' theorem and its application to conditional probability
  • Prior and posterior probabilities in Bayesian inference
  • Likelihood calculation using the binomial distribution (or multiplication rule for independent events)
  • The assumption of independence between draws (or sampling with replacement)
  • Connection to A/B testing: updating beliefs about which variant is better based on observed outcomes
  • Sanity check: posterior probability should be less than prior if the observed data is less likely under that hypothesis

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