Question

Police lineups either have a guilty suspect (the person who committed the crime) or an innocent suspect (not the person who committed the crime), and the witness either identifies or fails to identify the suspect. (Sometimes witnesses identify a suspect even if they are innocent, unfortunately.) Out of all the lineups conducted at a certain police station:

35% (.35) of the suspects were guilty, and 65% (.65) were innocent.

40% (.40) of the guilty suspects were identified.

5% (.05) of the innocent suspects were identified.

You know that a particular suspect was identified, and you are trying to figure out if they are guilty.

1. For the particular suspect that was identified in the lineup, which is more likely?

Select one:

a. The suspect is not guilty.

b. The suspect is guilty.

2. Refer to your answer on the previous question. How many times more likely is the option you selected, compared to the option you didn't select?

Write your answer as a number.

Answer 1

Let G and I denote the events that the suspect is guilty and that a witness identifies the suspect as guilty

P(G) = 0.35, P(G') = 0.65

P(I | G) = 0.40

P(I | G') = 0.05

Thus, P(I) = P(I | G)*P(G) + P(I | G')*P(G')

= 0.40*0.35 + 0.05*0.65

= 0.1725

Probability that a suspect is not guilty given that it was identified

= P(G' | I) = P(I | G')*P(G')/P(I)

= 0.05*0.65/0.1725 = 0.1884

Probability that a suspect is guilty given that it was identified

= P(G | I) = 1 - P(G' | I) = 0.8116

1) The event that the suspect is guilty is more likely

2) P(The suspect is guilty) = (0.8116/0.1884)*P(The suspect is not guilty)

-> P(The suspect is guilty) = 4.3*P(The suspect is not guilty)

The option selected is 4.3 times more likely than the option you didn't select