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There's a similar problem with three closed doors, one of which contains a prize behind it. You are asked to choose a door, and then shown one of the two remai

There's a similar problem with three closed doors, one of which contains a prize behind it. You are asked to choose a door, and then shown one of the two remaining doors which does NOT contain the prize. The question is should you switch doors, given the opportunity? What is the probability that of getting the prize if you switch, and if you don't switch? To illustrate, let A, B, C be doors, and door C be the door with the prize. You choose door A; the host tells you the prize is not in door B. What is the probability you will get the prize if you switch your door?

necubi 16y ago
No, this problem is different, and has a different solution. In your problem it makes sense to switch when given the choice, whereas in this one it does not. With the three doors you're given additional information once you choose a door, which allows you to choose a door with 1/2 probability of being right, rather than the 1/3 chance you started out with. In this problem you are given no additional information, so the probability of choosing the right envelope is the same when given a choice to switch as it is at the beginning (i.e., 1/2).
- mirkules 16y ago
  Actually, your probability of choosing the right door is 2/3 if you switch. I agree though that this problem is not the same, it just reminded me of it -- I guess you could say it's a similar class of problems.
InclinedPlane 16y ago
It's similar in that it's easy to fool people into thinking about the problem incorrectly and coming up with the wrong conclusion. People are very touchy about the monty hall problem and will refuse to believe that it's better to switch, even when confronted with numerical simulations of the problem. As for this problem, it's more of a riddle than a paradox, the reasoning is erroneous but you may not realize that if you're not careful. It's more similar to the 1 = 0 riddle or the 3 guys paying $10 dollars for rent riddle, tricking you into making a mathematical error that isn't immediately obvious.

necubi 16y ago

No, this problem is different, and has a different solution. In your problem it makes sense to switch when given the choice, whereas in this one it does not. With the three doors you're given additional information once you choose a door, which allows you to choose a door with 1/2 probability of being right, rather than the 1/3 chance you started out with. In this problem you are given no additional information, so the probability of choosing the right envelope is the same when given a choice to switch as it is at the beginning (i.e., 1/2).

mirkules 16y ago
Actually, your probability of choosing the right door is 2/3 if you switch. I agree though that this problem is not the same, it just reminded me of it -- I guess you could say it's a similar class of problems.

InclinedPlane 16y ago

It's similar in that it's easy to fool people into thinking about the problem incorrectly and coming up with the wrong conclusion. People are very touchy about the monty hall problem and will refuse to believe that it's better to switch, even when confronted with numerical simulations of the problem. As for this problem, it's more of a riddle than a paradox, the reasoning is erroneous but you may not realize that if you're not careful. It's more similar to the 1 = 0 riddle or the 3 guys paying $10 dollars for rent riddle, tricking you into making a mathematical error that isn't immediately obvious.