Estimate fake-account prevalence with capture-recapture

Two independent detectors flag suspected fake accounts on a platform of 50M active accounts. In a week, Detector A flags 12,000, Detector B flags 9,000, with 2,000 overlap. (a) Using the Chapman capture–recapture estimator, estimate total fake accounts and a 95% CI, stating assumptions. (b) How do correlated detectors or coordinated adversaries bias the estimate, and how would you reduce bias (e.g., stratification by region, account age, or activity band)? (c) If detector recall improves for high-activity accounts, propose a post-stratified or model-based adjustment and show the updated estimator at a high level.