Achieve 0.95 precision via thresholding

You must deploy a classifier on an imbalanced dataset (50,000 samples; ~5% positives). Product requires test-set precision ≥ 0.95 for the positive class. 1) Train any probabilistic model; on a held-out validation set, compute the precision–recall curve and select the smallest probability threshold τ achieving precision ≥ 0.95 while maximizing recall (break ties by higher recall, then by lower threshold). 2) Fix τ and evaluate once on the untouched test set; report precision, recall, number of predicted positives, and the expected number of false positives if you flag 1,000 items. 3) If no τ on validation attains 0.95 precision, propose two actionable strategies (e.g., abstain/top-k policy, recalibration, different model or features) and explain risks. 4) Provide sklearn-style code to search τ (using precision_recall_curve or make_scorer with a custom threshold) without leaking test data. 5) Explain how class imbalance and calibration affect your ability to meet the precision constraint and why optimizing ROC AUC would be misleading here.