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Sig·Software Engineer·Technical Phone Screen·Junior

Junior
May 2026

Summary

Quant researcher interview at Sig with a probability question built around a table of bookstore profit data. Pretty niche setup but the underlying concept is just conditional probability, which I should have been more comfortable with.

Questions Asked (1)

Q1

You're given a table of annual profits by sector at a university bookstore across multiple years. If you sample a single (sector, year) cell uniformly at random and the profit in that cell exceeds $8,000, what's the probability the year was 2019?

Product Analytics & MetricsAlgorithms & Data Structures
Author's notes

Blanked for a second on how to set it up.

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AI HintsAI Generated

Suggested Approach

Recognize this as a conditional probability problem: P(Year=2019 | Profit > 8000) = P(Year=2019 and Profit > 8000) / P(Profit > 8000). Compute the numerator by counting cells in 2019 with profit > 8000, and the denominator by counting all cells with profit > 8000. Then divide and express as a probability.

Pro tip: Always clarify whether the sampling is uniform over all cells or only over cells meeting the condition; the problem states uniform over all cells, so the denominator must include all qualifying cells across all years. Also, if the table is large, mention that you'd use a script or SQL query to avoid manual errors.

1. Define the events

Let A be the event that the year is 2019, and B be the event that profit > $8,000. We want P(A|B).

2. Compute the numerator

Count the number of cells where year = 2019 AND profit > 8000. This is |A ∩ B|.

3. Compute the denominator

Count the total number of cells where profit > 8000 across all years. This is |B|.

4. Calculate the conditional probability

Divide the numerator by the denominator: P(A|B) = |A ∩ B| / |B|. If needed, convert to a percentage.

5. Sanity check and communicate

Verify that the counts are correct and that the probability is between 0 and 1. Explain the reasoning clearly, noting that the sample space is restricted to cells with profit > 8000.

Key Points to Mention

  • Conditional probability formula: P(A|B) = P(A ∩ B) / P(B)
  • Uniform sampling over all (sector, year) cells means each cell has equal weight
  • The numerator is the count of cells in 2019 with profit > 8000
  • The denominator is the total count of cells with profit > 8000 across all years
  • The result is a ratio of counts, not a ratio of probabilities unless normalized
  • If the table is large, use a programmatic approach (e.g., SQL, Python) to compute counts accurately

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