This is an old probability teaser which came up in the context of a mathematics blog I read recently: the Monty Hall problem.
It's interesting because:
- The answer to the teaser is demonstrably correct and yet (to most people) intuitively wrong;
- The reason that people calculate wrongly is that the correct answer is actually derived from the fact that one of the agents in the puzzle (the quiz master) is displaying knowledge about the system that the other (the contestant) does not have. People who guess wrongly about the teaser do not account for this difference in knowledge.
I learned a new word today: veridical.