Calculate Expected Users Linking Coinbase Wallets
Overview
This question evaluates competence with Bernoulli trials, binomial distributions, and expectation/probability calculations relevant to modeling independent user actions such as linking a digital wallet.
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Jul 12, 2025, 6:59 PM
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Coinbase Wallet Linking: Bernoulli/Binomial Setup
Scenario
You have n users, each independently asked to link a Coinbase wallet. Each user links with probability p (and does not link with probability 1 − p).
Questions
- What is the expected number of users who link their wallet?
- What is the probability that at least one user links a wallet?
- Given that at least one of users A or B links a wallet, what is the probability that both A and B link?
Notes
- Independence across users is assumed.
- Each user's link decision is a Bernoulli(p) trial.
Solution
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