A social-network platform wants to measure and control abuse. Five percent of users are classified as "bad" and, on average, each bad user sends ten times more friend-requests than a good user.

If 5 % of users are bad and each bad user sends 10× as many friend-requests as a good user, what is the probability that a randomly selected request came from a bad user? Using only existing event logs, propose a method to identify the likely bad users. Given additional features (e.g., request timing, acceptance rate), derive P(good | request) with Bayes’ theorem. If you must shrink the confidence interval of that probability estimate to one-tenth its current width, what changes in data collection or analysis would you make?

Apply Bayes rule, reason about class imbalance, increase sample size or variance-reduction, and design behavioral signals.

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