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Coinbase·Data Scientist·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Coinbase data science interview with a probability modeling question that felt more like a stats exam than anything I'd done before. The scenario was about feature adoption and they walked through three parts back to back, each building on the last.

Questions Asked (1)

Q1

You're modeling wallet feature adoption where each of n users independently adopts with probability p. Walk through: (a) the expected number of adopters, (b) the probability that at least one user adopts, and (c) given that at least one adopts, the probability that exactly two users adopt.

Product Analytics & MetricsA/B Testing & Experimentation
Author's notes

Part (a) was fine, np, done.

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AI HintsAI Generated

Suggested Approach

Recognize that the number of adopters follows a Binomial(n, p) distribution. For (a), use the expectation of a binomial. For (b), use the complement rule. For (c), apply the definition of conditional probability: P(X=2 | X≥1) = P(X=2) / P(X≥1).

Pro tip: After deriving the formulas, briefly discuss how you would estimate p from data (e.g., maximum likelihood) and how you might validate the independence assumption, as real-world adoption often exhibits clustering.

1. Define the random variable

Let X be the number of users who adopt the wallet feature. State that X ~ Binomial(n, p) under the independence assumption.

2. Compute expected adopters

For a binomial distribution, E[X] = n * p. This is the expected number of adopters.

3. Compute probability of at least one adopter

Use the complement: P(X ≥ 1) = 1 - P(X = 0) = 1 - (1-p)^n.

4. Compute conditional probability of exactly two adopters

Apply conditional probability: P(X=2 | X≥1) = P(X=2) / P(X≥1). Compute P(X=2) using the binomial PMF: C(n,2) * p^2 * (1-p)^(n-2). Then divide by the result from step 3.

5. Interpret and discuss assumptions

Relate the results to the business context (e.g., expected adoption, likelihood of any adoption). Mention that independence may not hold in practice and suggest ways to check or adjust.

Key Points to Mention

  • Binomial distribution assumptions: fixed n, independent trials, constant probability p.
  • Expected value formula for binomial: E[X] = n * p.
  • Complement rule for 'at least one' probability: P(X ≥ 1) = 1 - (1-p)^n.
  • Binomial PMF: P(X = k) = C(n, k) * p^k * (1-p)^(n-k).
  • Conditional probability definition: P(A|B) = P(A ∩ B) / P(B).
  • Practical considerations: estimating p from data, checking independence, and handling overdispersion.

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