You are testing a biometric algorithm that warns security at the airport if someone has been flagged for a second screening. The test has a 99% sensitivity (true positive probability), 99% specificity (true negative probability), but only 0.5% of people have been flagged.
a) Using Bayes theorem where the test is P(+|Flagged) = 0.99, P(-|Not-Flagged), P(Flagged) = 0.005, and P(+) = P(+|Flagged)P(Flagged) + P(+|Not-flagged)P(Not-flagged). What is the probability that a randomly selected person that tested positive on the biometric test has been flagged, P(Flagged|+)?
b) The spec for your biometric system requires requires a P(Flagged | +) value of greater than 45% to be acceptable by the public, what do the sensitivity and specificity values need to be to meet that spec?
You can either do this manually or using an excel spreadsheet.