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Pastimes : Let's Talk About Our Feelings!!!
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To: nihil who wrote (33635)4/4/1999 1:01:00 AM
From: Chuzzlewit  Read Replies (1) of 108807
 
There were only two souls brave enough to try this one, and I disagree with their answers. I believe the answer is you must always switch, and once you see the reasoning I think the answer will appear simple.

Suppose we label the curtains A, B, and C for convenience. In each case you initially choose curtain A.

Suppose the RR is behind A. Switching will lose.

But suppose the RR was behind curtain B, Monte eliminates curtain C and so you choose curtain B. Switching will win.

Now suppose the RR was behind curtain C, Monte eliminates curtain B and so you choose curtain C. Switching wins.

Another way to think about it:

Initially, the probability of choosing the correct curtain is 1/3. So the probability that the RR is behind one of the two remaining curtains is 2/3. Since Monte always reveals a curtain that does not hide the RR, the probability that it is behind the remaining curtain is 2/3.

Note: revealing that one of the two remaining curtains was a loser does not increase the probability that your curtain (the original guess) was a winner, because there was a 100% chance that at least one of the remaining curtains was a loser.

This is counter-intuitive, but I believe that this is the correct solution.

TTFN,
CTC
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