Consider this scenario:
The city of Kalsville has a population very close to one million. For purposes of facile explanation of the scenario we will assume it to be precisely one million.
Detectives in Kalsville are working on a crime and have put together a description of the perpetrator, based on things such as height, a tattoo, a limp, an earring. The crime itself was committed in such a way, that no visitor from outside the city could have committed it. Let us assume that only one person in 10,000 fits the description. On a routine patrol the next day, police officers see a person fitting the description. The person is arrested and brought to trial solely on the fact that he fits the description.
During the trial, the prosecutor tells the jury that since only one person in 10,000 fits the description (a true statement), it is highly unlikely (far beyond a reasonable doubt) that an innocent person fits the description (again a true statement), and therefore it is highly unlikely that the defendant is innocent.
If you were a member of the jury, would you cast a "guilty" vote?
If yes, what is your level of confidence?
If no, what is wrong with the prosecutor's reasoning?
Note: For the purposes of the problem, assume that the law-enforcement, legal, and judicial authorities in Kalsville follow the same legal and juridical provisions governing all well-known U.S. cities.
*** Adapted from an original problem by David Morin.