# A defendant is found guilty or not guilty

Statisticians are familiar with variation, as are forensic scientists who observe it in the course of their work. Lawyers, however, prefer certainties. A defendant is found guilty or not guilty' (Aitken 1995 p. 5). How do statistics and probability assist in the interpretation of evidence, and what are the problems that may arise when probability is introduced 'in the courtroom'? Statistics and probability assist in the interpretation of evidence in many ways, and can be both useful and confusing.

In this essay I plan to look at a brief history of statistics and probability, as this will help to better define what they are and how they are used in a legal sense. I will also look at cases to determine the pros and cons of both statistics and probability, showing them at their most helpful, and also at their worst (such as in the Sally Clarke case). I believe this will help me to critically analyse them, and therefore answer the question better.

Probability is the chance of something happening and the number of ways in which it can occur. In maths, it is called the "Probability Theory", and determines the likelihood using random variables, random processes and events (random or statistical). For example, tossing a coin once would produce a random result. However, if you repeated it many times, eventually a statistical pattern would appear from the randomness, allowing you to predict the result using probability.

An Italian mathematician named Gerolamo Cardano in the 16th century, as he attempted to analyse games of chance, first discovered this, and Pierre de Fermat and Blaise Pascal continued his work in the 17th century, eventually becoming the founders of the Probability Theory… In 1654 one of Pascal's friends, the Chevalier de Mi?? ri?? approached him with a gambling problem. He and the other player wanted to finish their game earlier, and given the current circumstances of the game, wanted to divide the stakes fairly, based on the chance each had of winning the game from their current point.

Pascal collaborated with Fermat and, from their discussion the notion of expected value (or mean) was born. (David, 1962) describes how Pascal and Fermat's discussion on "the problem of points" evolved: "the starting insight for Pascal and Fermat was that the division should not depend so much on the history of the part of the interrupted game that actually took place, as on the possible ways the game might have continued, were it not interrupted.

" For example, it's obvious that a player with a 6-4 lead in a game to 10 has the same chance of eventually winning as a player with a 16-14 lead in a game to 20, and Pascal and Fermat therefore thought that interruption in either of the two situations ought to lead to the same division of the stakes. In other words, what is important is not the number of rounds each player has won so far, but the number of rounds each player still needs to win in order to achieve overall victory.

Pascal and Fermat's work eventually provided the foundations for the modern probability theory, which was advanced by Russian mathematician, Andrey Kolmogorov in the 1930's, and became the theory we know today. Probability Theory is helpful in court cases as it allows the prosecution and the defence to look at the chance of the accused being innocent or guilty from both sides of the argument using probability to assist them.