What are the chances that the DNA on the knife came from someone other than the suspect?
A man has been stabbed to death at his home in a city, and a suspect is on trial for the crime. The murder weapon has been recovered, and a sample of DNA has been obtained from the handle. The suspects DNA profile matches that on the handle. An expert witness says that the probability of anyone else being a DNA match is 1 in 3 million.
A. 1 in 3 million B. More than 1 in 3 million C. Less than 1 in 3 million D. We don't have enough information to say
1 in 3 million is the likelihood that any innocent person in the population has a DNA profile matching that found on the knife.
If the population is greater than 3 million (as an example, the UKs population is around 60 million), more than 1 person will have that profile.
Hence, the odds that the DNA on the knife did not come from the suspect must be higher than 1 in 3 million.
If you thought the odds were 1 in 3 million, you fell for the Prosecutors Fallacy.