Ever since the "Prior Confusion" post I was planning to formulate one of its paragraphs as the following abstract puzzle, but somehow it took me 8 years to write it up.
According to fictional statistical studies, the following is known about a fictional chronic disease "statistite":
- About 30% of people in the world have statistite.
- About 35% of men in the world have it.
- In Estonia, 20% of people have statistite.
- Out of people younger than 20 years, just 5% have the disease.
- A recent study of a random sample of visitors to the Central Hospital demonstrated that 40% of them suffer from statistite.
Mart, a 19-year Estonian male medical student is standing in the foyer of the Central Hospital, reading these facts from an information sheet and wondering: what are his current chances of having statistite? How should he model himself: should he consider himself as primarily "an average man", "a typical Estonian", "just a young person", or "an average visitor of the hospital"? Could he combine the different aspects of his personality to make better use of the available information? How? In general, what would be the best possible probability estimate, given the data?