How many shoplifters will be correctly identified

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Reference no: EM133385382

Case Study: Assume that the facial recognition software has a hit rate is 90% and the false positive rate is 10%. (Here's what I mean: Assume Bob Jones is a known shoplifter with an image on file. If Bob Jones enters the store, the software will match him to his picture 90% of the time. That's a hit because the software made a correct match. If Jim Garcia looks sort of like Bob Jones, he might be accidentally matched with Bob Jones. That's a false positive because the software matched an innocent person with a known shoplifter. This kind of error happens about 10% of the time.)

Prior Probability: Assume that 1 in 500 people is a known shoplifter.
Here's the question: If a match is made, how likely is it that person is actually a shoplifter? (Would Walmart be wasting time and money following these people around?)
Let's do the math using a sample of 10,000 people.
Of the 10,000 people, how many will be known shoplifters?

Question:

  • How many shoplifters will be correctly identified? (Use the hit rate.)
  • Of the 10,000 people, how many will be innocent?
  • How many innocent people will be incorrectly identified as shoplifters? (Use the false alarm rate.)
  • In all how many people will be identified as shoplifters?
  • What percentage of these people will be actual shoplifters?
  • How many shoplifters would go undetected?

 

Reference no: EM133385382

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