The Monty Hall Problem, Continued

I suppose one comment for my very first blog entry is to be considered good. To recap, I gave a new wording to the famous Monty Hall problem. Three cups were placed upside down on a bar desk, with a $100 bill under one of them. You were told to chose one of the cups, and if that particular cup contained the $100 bill, the bill would be yours. I lifted one of the other cups after watching you choose one, revealing that there was no bill under that one. You were offered an opportunity to change your mind and go for the other unrevealed cup instead of the one you initially chose. The question is: Should you switch or should you stay with your initial choice?

Anonymous commented as follows:
You should switch. The probability that you picked the right cup first is 1/3, so its 2/3 that the bill is in one of the other cups. Knowing that the cup is not in one of them doesnt change that. If you switch the probability is 2/3.
This may seem counter-intuitive to many readers. But from a probabilistic point of view, it seems to make sense. This is the answer that I expected from most readers who are already familiar with the Monty Hall problem, since this is the correct answer to the problem in its basic formulation. However, remember that I hinted that there is a twist to this one? There is, and this answer is, in fact, wrong. You should stay with your initial choice.

Now, I expect to be ridiculed by some of my readers. Please, shoot. I'm very confident that my solution is correct, and I will explain why in a later entry. In the meantime, can anyone come up with an explanaition? Why should you stay? Or, if you don't agree with me, why am I wrong?

2 comments:

Valterego said...

You shouldn't change because in Sweden we learn that it will always getting worse by changing. Most of all we can see this when changing to a shorter queue to the counter in the supermarket.

Or not.

btw, i love this blog :-)

//E

Economatheek said...

Also, we don't want to insult the cash administrator by changing queues. =)

Thank you, Valterego.

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