Calculate Posterior Probability of Flagged User Being Bad Actor

##### Scenario Platform must distinguish good users from potential bad actors using Bayesian inference while controlling error rates. ##### Question Given a prior probability p of a user being a bad actor and classifier outputs with known true-positive and false-positive rates, derive the posterior probability that a flagged user is truly bad. Define Type I and Type II errors in this context and explain their business impact. If 1 % of 10 million users are truly bad and the classifier has 95 % recall and 2 % false-positive rate, calculate the expected number of bad actors caught and the expected number of good users incorrectly flagged. ##### Hints Apply Bayes’ theorem, build a 2×2 confusion matrix, compute expected counts from prevalence and error rates.