## Probability in Criminal Justice

Criminal justice has come a long way since the days of pens and quills, when a man’s fate could be decided on a whim by a judge’s intuition. With the development of forensics, recorded media, and powerful background checking techniques, today’s courts emphasize facts above all else. Of course, solid evidence is always the best way to convict a criminal, but some things can never be said for certain. Witness testimony, for example, while potentially one of the most compelling sources of testimony, is based solely on the word of another person who may or may not present the correct information. Even with all of our modern technology in forensic analysis, certain correlations and claims are always left to some degree of chance. For instance, a trial in Georgia convicted one Wayne Williams for the murder of two men based on probabilistic evidence linking the similarity of fibers on the victims’ bodies to fibers in Williams’ home and car. Below is a hypothetical simplified analysis of the conclusions in the Georgia court. (the below example is purely hypothetical for the purpose of demonstration and does not reflect that actually happened in the Williams case)

Suppose two men were murdered in an office building, and suppose Williams regularly frequented the office building as part of his job such that at any given moment he could be found in the building with probability 0.1.  If Williams was at the scene of the crime, fiber matching would return positive with probability 1. However, since forensic analysis is not perfect, even if Williams was not at the crime scene, the matching test would return positive with probability 0.01.

Let S = Williams was at the scene of the crime

Let F = Forensics indicates that fibers found on the murdered men match fibers in Williams’ clothes

P(S | F) = P(S) * P(F | S) / P(F)

= P(S) * P(F | S) / (P(S) * (F | S) + P(~S) * (F | ~S)

P(S | F) = 0.1 * 1 / (0.1 * 1 + 0.9 * 0.01) = 0.917

From these results we can conclude that given that the fiber matching returned positive, there is a ~92% chance that Williams was at the crime scene. Coupled with other evidence such as motivation and timing, placing Williams at the crime scene with such high probability is compelling evidence. We can see from this analysis that although Williams only spends about 1/10 of his time at the scene of the crime, it is reasonable to assume he was at the crime scene conditional on the information that the fiber match returned positive.

Some may argue that probability is a poor tool to use in a context as serious as criminal justice because of its undeterministic nature, and they may have a point that these techniques do produce mistakes, raising the ethical question of whether or not the court should adhere to them. However there is no denying the usefulness of this kind of analysis, and in any case it provides information where information is needed to make a decision. Would you rather let 15 criminals go to spare one man a false sentence, or unjusty put an innocent man behind bars in order to convict 15 criminals?

http://digitalarchive.gsu.edu/cgi/viewcontent.cgi?article=2236&context=gsulr

-cosmomonkey37