## What A Random Match Probability Is

It is important to realize what a random match probability is not. It is not the chance that someone else is guilty or that someone else left the biological material at the crime scene. Likewise, it is not the chance of the defendant not being guilty or the chance that someone else in reality would have that same genotype. Rather a random match probability is simply the estimated frequency at which a particular STR profile would be expected to occur in a population. This random match probability may also be thought of as the theoretical chance that if you sample one person at random from the population they will have the particular DNA profile in question.

Switching the language and meaning of a random match probability is something referred to as the Prosecutor's Fallacy or the fallacy of the transposed conditional (Thompson and Schumann 1987, Balding and Donnelly 1994). Statements such as 'there is only a 1 in 17000 chance that the DNA profile came from someone else' or 'there is only a 1 in 17000 chance that the defendant is not guilty' are examples of the prosecutor's fallacy. A correct statement would be 'the probability of selecting the observed profile from a population of random unrelated individuals is expected to be 1 in 17 000 based on the alleles present in this sample...' Note that with a 13 STR locus-match instead ofjust the three used in the above example the random match probabilities are in the range of trillions, quadrillions, and beyond (see Table 21.2 and D.N.A. Box 21.1).

The Defense Attorney's Fallacy is equally problematic where the assumption is made that everyone else with the same genotype has an equal chance of being guilty or that every possible genotype in a mixture (see Chapter 22) has an equal chance of having committed the crime (NRC II, p. 133). Access to the crime scene, motive, and legitimate alibis all play a role in an investigation suggesting that it is unwise to consider DNA evidence and corresponding frequency estimates in a vacuum devoid of other information. A suspect is usually under suspicion and investigation prior to knowing his DNA profile, and thus the DNA results are most often used to corroborate and connect a criminal perpetrator to his crime scene rather than as the sole evidentiary material.