How many shoplifters will be correctly identified

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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