A data scientist is evaluating different binary classification models. A false positive result is 5 times more expensive (from a business perspective) than a false negative result. The models should…

Question

Exhibit

Options

• ATN = 91, FP = 9
• BTN = 99, FP = 1
• CTN = 96, FP = 4
• DTN = 98, FP = 2

• A
  29% (11)
• B
  5% (2)
• C
  16% (6)
• D
  50% (19)

Explanation

Option D (TN=98, FP=2) satisfies all three criteria simultaneously: its false positive rate of 2% (FP=2 out of 100 total negatives) is well within the ≤10% threshold, and among the valid candidates, its low FP count minimizes business cost since each false positive carries a 5x penalty - making the weighted cost function (5×FP + 1×FN) smallest when FP is minimized without sacrificing the recall requirement.

Why each distractor fails:

• Option A (FP=9): Technically passes the FPR threshold at 9%, but with the highest false positive count of all options, it produces the greatest business cost (5×9 = 45 FP-cost units), making it suboptimal.
• Option B (FP=1): While it has the lowest FP count, a model this conservative (rarely predicting positive) typically fails the recall ≥ 80% requirement - it misses too many true positives by being overly restrictive.
• Option C (FP=4): Passes FPR at 4%, but with a higher FP cost (5×4 = 20) than Option D (5×2 = 10), it doesn't minimize business costs when a better-performing model exists.

Memory tip: Think "FP tax" - when false positives are penalized heavily, you want the lowest FP that still keeps recall high enough. Picture a sliding threshold: push it too far to avoid FP (like B) and you lose recall; leave it too loose (like A) and you pay a heavy cost penalty. The sweet spot is D.

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