Due to new techniques of scientific analysis of evidence, mathematical calculations are more and more present in the courtroom. However, because judges and juries are often not equipped to understand these calculations or the significance of their results, these methods can lead to serious miscarriages of justice. In this lecture, we will explain on astonishing examples how ordinary intuition can lead us astray, and describe some cases of dramatic mathematical errors in trials. Finally, we will give an interactive presentation of Bayesian analysis, a method to combine pieces of interdependent evidence that may be of widely different types in order to provide a reasonable probability range.