Instacart·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026Remote

Summary

Instacart SWE interview with a probability/simulation coding question that was more stats-heavy than I expected. Not your typical leetcode grind.

Questions Asked (1)

Implement a function that estimates, via Monte Carlo simulation, the probability that an athlete will beat their personal best on a future attempt at a given event, based on their historical attempt scores.

Algorithms & Data StructuresA/B Testing & ExperimentationTechnical Trade-offs

Author's notes

I knew Monte Carlo at a surface level but hadn't thought about fitting a distribution to empirical data on the fly.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem: define the athlete's historical scores, the personal best, and the event distribution. Then outline a Monte Carlo simulation that samples future attempts from a fitted distribution (e.g., normal) and estimates the probability of exceeding the personal best, while discussing statistical assumptions and trade-offs.

Pro tip: Mention that you would validate the simulation by comparing with a theoretical probability (e.g., using the normal CDF) and discuss how to handle small sample sizes or non-normal data, showing awareness of real-world data issues.

1. Clarify the problem and inputs

Define the historical attempt scores, the personal best, and the number of future attempts. Ask about the distribution of scores and whether independence can be assumed.

2. Choose a probabilistic model

Decide on a distribution to model future attempts (e.g., normal, log-normal) based on historical data. Estimate parameters (mean, variance) from the sample.

3. Implement Monte Carlo simulation

Simulate many future attempts by sampling from the chosen distribution. For each simulation, check if the attempt exceeds the personal best and record the outcome.

4. Estimate probability and assess uncertainty

Compute the proportion of simulations where the personal best is beaten. Provide a confidence interval or standard error to quantify simulation uncertainty.

5. Discuss trade-offs and extensions

Address assumptions (e.g., independence, distribution choice), computational cost vs. accuracy, and potential improvements like bootstrapping or Bayesian methods.

Key Points to Mention

Monte Carlo simulation basics: random sampling, repeated trials, and probability estimation.
Choice of probability distribution (e.g., normal) and parameter estimation from historical data.
Independence assumption and its limitations (e.g., athlete improvement over time).
Handling small sample sizes: bootstrapping or using a prior.
Computational trade-offs: number of simulations vs. accuracy, and variance reduction techniques.
Validation: comparing simulation results with analytical solutions or known cases.

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