Compute posterior spam risk from flags

A binary classifier flags requesters as spam. Last week, 12% of all requesters were spam. The classifier's true positive rate (TPR) is 0.90 and its false positive rate (FPR) is 0.04. a) Apply Bayes' theorem to find $P(\text{Spam} \mid \text{Flagged})$. Show the formula and give the final numeric value rounded to 4 decimal places. b) Find $P(\text{Spam} \mid \text{Not Flagged})$ and explain what it means: among requesters who are not flagged, what share are still spam? c) Suppose the base rate falls to 6% while TPR and FPR stay the same. Recalculate $P(\text{Spam} \mid \text{Flagged})$. Briefly describe how changes in the base rate affect the posterior and why. Show all steps, formulas, and final answers. Overview: This problem tests Bayes' theorem, conditional probability, and how to interpret classifier metrics (true positive and false positive rates) when computing posterior spam risk.