### Home > CCA2 > Chapter Ch12 > Lesson 12.1.3 > Problem12-48

12-48.

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.

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

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?

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

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.