Probability Calculus, Pitfalls of Intuition and Judicial Errors

In the last decades the powerful of the laboratories’ analytical results to highlight the dynamic of criminal acts has been object of an increasing attention, partly because of the enormous potentiality of the DNA test that has transformed forensic sciences. Statistics is assuming a fundamental role in forensic science, in particular to quantify the probative value of traces collected at the crime scene, or on individuals suspected to be involved in a crime, and analysed by forensic laboratories. Results of comparative analyses (comparative in the sense that some characteristics of traces recovered at the crime scene are compared to those of material originating from the suspect) are generally presented in numeric form, mostly in probability terms, and need to be carefully interpreted. Moreover, the scientific evidence collected at the crime scene must be considered in conjunction with the bulk of informations the court possesses about the case. Judicial errors correlated to an improper use and interpretation of probability calculus have originated a large debate about (1) how the probative value of the traces is computed, (2) how to interpret the statistical expertise at trial, and (3) how the probative value of the scientific evidence can be combined with the other sources of information (for example, a witness statement) in view of the court decision. Starting from a general description of the potential scenario of interest (section “The Evaluation of Scientific Evidence”), followed by a non exhaustive overview (section “Pitfalls of Intuition”) of the possible errors of interpretation that can be originated by intuition which may be a bad substitute of the laws of probability calculus, this paper shows (section “The Transition: Bayes’ Theorem”) how the Bayes’ theorem can represent a formidable tool to combine in a rational way the different sources of information that may become available at trial.