Editing Base rate fallacy (section)

===Example 4: biological testing of a suspect===
A crime is committed. Forensic analysis determines that the perpetrator has a certain blood type shared by 10% of the population. A suspect is arrested, and found to have that same blood type.

A prosecutor might charge the suspect with the crime on that basis alone, and claim at trial that the probability that the defendant is guilty is 90%.

However, this conclusion is only close to correct if the defendant was selected as the main suspect based on robust evidence discovered prior to the blood test and unrelated to it. Otherwise, the reasoning presented is flawed, as it overlooks the high [[prior probability]] (that is, prior to the blood test) that he is a random innocent person. Assume, for instance, that 1000 people live in the town where the crime occurred. This means that 100 people live there who have the perpetrator's blood type, of whom only one is the true perpetrator; therefore, the true probability that the defendant is guilty – based only on the fact that his blood type matches that of the killer – is only 1%, far less than the 90% argued by the prosecutor.

The prosecutor's fallacy involves assuming that the prior probability of a random match is equal to the probability that the defendant is innocent. When using it, a prosecutor questioning an expert witness may ask: "The odds of finding this evidence on an innocent man are so small that the jury can safely disregard the possibility that this defendant is innocent, correct?"<ref>{{Cite journal |last1=Fenton |first1=Norman |last2=Neil |first2=Martin |last3=Berger |first3=Daniel |date=June 2016 |title=Bayes and the Law |journal=[[Annual Review of Statistics and Its Application]] |volume=3 |issue=1 |pages=51–77 |bibcode=2016AnRSA...3...51F |doi=10.1146/annurev-statistics-041715-033428 |pmc=4934658 |pmid=27398389}}</ref> The claim assumes that the probability that evidence is found on an innocent man is the same as the probability that a man is innocent given that evidence was found on him, which is not true. Whilst the former is usually small (10% in the previous example) due to good [[forensic evidence]] procedures, the latter (99% in that example) does not directly relate to it and will often be much higher, since, in fact, it depends on the likely quite high [[prior odds]] of the defendant being a random innocent person.