Model Feature Adoption Probability for Users
Overview
This question evaluates understanding of basic probability concepts such as the binomial distribution, expectation, and conditional probability in the Statistics & Math domain, assessing a candidate's ability to model and reason about discrete random variables.
Coinbase
Aug 4, 2025, 10:55 AM
Data Scientist
Technical Screen
Statistics & Math
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Feature Adoption Probability Modeling
Context
You are analyzing adoption of a new wallet feature. Each of n users independently adopts the feature with identical probability p. Let X be the number of adopters among the n users.
Tasks
(a) Compute the expected number of adopters.
(b) Compute the probability that at least one user adopts.
(c) Given that at least one user adopts, compute the probability that exactly two users adopt.
Hints
- Model X with a Binomial(n, p) distribution.
- Use the complement rule for "at least one": P(X ≥ 1) = 1 − P(X = 0).
- Use conditional probability: P(A | B) = P(A ∩ B) / P(B).
Solution
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