The answer is: the guest should switch his choice, anyway.
The probability the guest wins the lottery if he does not switch his choice is 1/3 and the probability he loses if he does not switch is 2/3
On the other hand, the probability the guest wins the lottery if he switches his choice is 2/3 and the probability he loses is 1/3
The reason I will state later. I have a simple solution for this question.
Now consider a generalization. There are n boxes in front of the guest. Follow the same procedure. What is the probability the guest wins the lottery if he does not swtich his choice and what is the probablity he wins if he switches his choice?
The problem is, is there a intuitive, obvious thought lead to the correct solution?
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