There are three caves, two of which contain dragons and one of which is a hiding...

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)?

Solutions

Expert Solution

Let A,B,C be the three caves and A be the one chosen by the prince initially.

Let be the event that cave i has the princes,i=A,B,C and S be the event that cave C has been revealed of having a dragon.

Therefore, the prince will have higher probability of finding the princes if he switches his choice to cave B.

Let A,B,C,D be the three caves and A be the one chosen by the prince initially.

Let be the event that cave i has the princes,i=A,B,C,D and be the event that cave i has been revealed of having a dragon,i=A,B,C,D.

Suppose C and D are the caves that has been revealed.

Therefore, the prince will have higher probability of finding the princes if he switches his choice to cave B.

orchestra answered 1 year ago

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