Question 2

There has been a great deal of controversy over the last several years regarding what types of surveillance are appropriate to prevent terrorism. Suppose a particular surveillance system has a 95% chance of correctly identifying a future terrorist and a 99.9% chance of correctly identifying someone who is not a future terrorist. If there are 1,000 future terrorists in a population of 400 million, and one of these 400 million is randomly selected, scrutinized by the system, and identified as a future terrorist, what is the probability that he/she actually is a future terrorist? (Round your answer to six decimal places.)

Scenario: There has been a great deal of controversy over the last several years regarding what types of surveillance are appropriate to prevent terrorism.

Events:

  • - The system identifies someone is a future terrorist.
  • - A randomly selected person is a future terrorist.
  • - A randomly selected person isn't a future terrorist.

Probabilities:

  • .
  • .
  • .

Problem: If someone in a population of 400 million is randomly selected, scrutinized by the system, and identified as a future terrorist, what is the probability that he/she actually is a future terrorist? Does the value of this probability make you uneasy about using the surveillance system?

Process: The question can be rephrased to ask what the probability is of someone being a future terrorist given that the system identified them as a future terrorist. This would be the conditional probability . Since we know the conditional probability , we can use Bayes' Theorem. We have to find the probability using the law of total probability.

Answer: 0.00237. Since the probability is less than 0.05, it is unlikely that people "flagged" as terrorists would be actual terrorists in this scenario.