MLA-C01 Question #114: Real Exam Question with Answer & Explanation

Question

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 be evaluated based on the following criteria: 1) Must have a recall rate of at least 80% 2) Must have a false positive rate of 10% or less 3) Must minimize business costs After creating each binary classification model, the data scientist generates the corresponding confusion matrix. Which confusion matrix represents the model that satisfies the requirements?

Options

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

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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