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Calculate Expected Users Linking Coinbase Wallets

CoinbaseData Scientist · Technical Screen
EasyData ScientistTechnical ScreenStatistics & Math

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Coinbase probability question covering Bernoulli indicators, expected wallet links, complement rule for at least one success, and conditional probability for two users linking wallets.

Scenario

When users sign up for Coinbase, each of the n users is independently prompted to link a crypto wallet. Each user links their wallet with probability p (and fails to link with probability 1 − p), independently of every other user.

Question

Using this model, answer the following:

  1. What is the expected number of users who link their wallet?
  2. What is the probability that at least one of the n users links a wallet?
  3. For two specific users A and B, given that at least one of A or B links a wallet, what is the probability that both A and B link their wallets?
Hints
  • Part 1: Use linearity of expectation with indicator variables — you do not even need independence here.
  • Part 2: Use the complement rule; it is easier to compute the probability that no one links.
  • Part 3: Use the definition of conditional probability, P(A ∩ B | A ∪ B) = P(A ∩ B) / P(A ∪ B).