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Question 6 (20 points) Recall the Monty Hall problem as presented in class. There are three caves, two of which contain dragons and one of

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Question 6 (20 points) 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. 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. Question 6 (20 points) 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. 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

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