Problem preview

S-MD.7 Core M3-055-R08-V02

Analyze decisions and strategies using probability concepts in more complex settings.

Interpret false positives with base rates

Problem

For \(2,000\) transactions with \(4\%\) fraud, \(75\%\) sensitivity, and \(10\%\) false-positive rate, compute fraud and nonfraud counts, true and false flags, total flags, and \(P(\text{fraud}~|~\text{flag})\).

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Use all 80 fraud cases as true flags instead of 75%, plus 192 false flags, for 272 flags and posterior 80/272.

Use sensitivity 75% as posterior; with 60 true and 192 false flags, ignore the total 252 denominator.

There are 60 true flags and 192 false flags, for 252 flags; P(fraud|flag)=60/252=5/21.

Use 1920 false flags instead of 10% of 1920; combine with 60 true flags for 1980 and report posterior 60/1980.

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Curriculum context

Course: Math III
Standard: S-MD.7
Category: Statistics and Probability
Domain: Using Probability to Make Decisions
Objective: Analyze decisions and strategies using probability concepts in more complex settings.
Problem type: Interpret false positives with base rates