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Sig·Software Engineer·Technical Phone Screen·Junior

Junior
Jun 2026

Summary

SIG quant engineer interview with a probability and statistics question pulled straight from a contingency table setup. Pretty focused, no fluff.

Questions Asked (1)

Q1

You're given a two-way contingency table from a survey of 1000 people, with exercise preference on one axis and age group on the other. How do you compute the conditional probability that a respondent is in the 33-37 age group, given that their preferred exercise is swimming?

Product Analytics & MetricsAlgorithms & Data Structures
Author's notes

Pretty mechanical once you see it.

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AI HintsAI Generated

Suggested Approach

First, clarify that you need the cell count for swimming and age 33-37, and the total count for swimming. Then compute the conditional probability as the ratio of that cell count to the swimming total, and explain the reasoning behind the formula.

Pro tip: Mention that this is a straightforward application of conditional probability, but in practice you'd also check for statistical significance and consider whether the sample size in the swimming category is large enough to draw reliable conclusions.

1. Identify the given condition

Determine the total number of respondents whose preferred exercise is swimming. This is the denominator of the conditional probability.

2. Identify the target event

Find the number of respondents who both prefer swimming and are in the 33-37 age group. This is the numerator.

3. Compute the conditional probability

Divide the count from step 2 by the count from step 1: P(Age 33-37 | Swimming) = (count of swimming and 33-37) / (total count of swimming).

4. Interpret the result

Express the probability as a decimal or percentage and explain what it means in the context of the survey.

Key Points to Mention

  • Conditional probability formula: P(A|B) = P(A and B) / P(B)
  • The denominator is the marginal total for the given condition (swimming), not the overall total of 1000.
  • The numerator is the joint frequency of both conditions (swimming and age 33-37).
  • Ensure the table is properly structured with row and column totals to easily extract these counts.
  • Consider discussing potential pitfalls like small sample sizes in the swimming category or misinterpreting the direction of conditioning.
  • Mention that this is a basic calculation but could be extended to test independence or compare across groups.

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