Governments and security companies are coming to rely more heavily on facial recognition software to locate persons of interest.

Consider a hypothetical situation. Suppose that facial recognition software can accurately identify a person $99.9\%$ of the time, and suppose the suspect is among $200,000$ facial images available to a government agency. When the software makes a positive identification, what is the probability that it is not the suspect?

1. Make a model for this situation.

   Hint (a):

   Use the model at right as a starting point.
   Complete it by including the probabilities.

   

   Hint 2(a):

   P(suspect) $=$ ¹/_200,000, P(ID is correct) $=0.999$
   P(not the suspect) $=$ ?, P(ID is not correct) $=$ ?

2. If a person has been identified as the suspect, what is the probability that he or she is not actually the suspect?

   Hint (b):

   $\text{Probability} =\frac{\text{# of desired outcomes}}{\text{# of possible outcomes}}$

   Hint 2(b):

   The desired outcome is a person who is not the suspect being incorrectly identified, or situation D.
   The possible outcomes are situation D and the suspect being correctly identified, or situation A.