In: Statistics and Probability
Recall the Monty Hall problem as presented in class. There are three caves, two of which contain dragons and one of which is a hiding princess. The prince chooses a cave and a wizard (truthfully) reveals to the prince that one of the other caves has a dragon. 2 The prince now has the option to switch to the other cave (the one he didn’t choose and wasn’t revealed to have a dragon), and try his luck finding the princess in that cave instead. (a) Explain why the prince should always switch caves. (b) Now suppose there are four caves, three of which contain a dragon and one of which contain a princess. After the prince makes his first choice, the wizard reveals two of the caves with dragons (separate from the one the prince chose originally). Should the prince stay or switch? Are the probabilities different than (a)?