Determine Probability of Friend Request Being Fake
Overview
This question evaluates understanding of conditional probability, base-rate reasoning, and probabilistic modeling of differing event rates. It is commonly asked to assess whether an applicant can integrate prior class proportions with unequal per-account event rates when estimating source probabilities, belongs to the Statistics & Math category, and tests conceptual understanding of probability rather than implementation-level skills.
Scenario
You operate a platform where 95% of accounts are real and 5% are fake. Fake accounts send 10 times as many friend requests per account as real accounts.
Question
If you receive a random incoming friend request, what is the probability that it is from a fake account?
Assumptions
- "10× more" means each fake account sends friend requests at a per-account rate 10 times that of a real account.
- You are equally likely to receive any given friend request (ignoring network structure or targeting effects).
Hint
Apply Bayes’ theorem: posterior ∝ prior × likelihood.
Solution
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