The Curious Prisoner Puzzle
Here’s an interesting riddle that is more complicated than it looks:
You wake up locked inside a room with no window. You know your captors have four facilities in the following locations: a Vulcan Mountain, a Vulcan Desert, an Earth Mountain, an Earth Desert. They flip a coin to decide which planet to send you to, then they flip a coin to decide which facility on that planet to use.
Wanting to know where you are, you try to get some information out of the guard. He refuses at first, but eventually he offers the following: “If you are on Vulcan, you are in the Mountain”. What are the chances that you are in the Vulcan Mountain facility?
(You can assume that the guard is telling the truth and not trying to intentionally manipulate the situation)