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That's not enough. You need the knowledge of "the organizer will ALWAYS open a door that contains a goat" to draw the conclusion of the article. That knowledge

• mcphage 12y ago
  > That's not enough. You need the knowledge of "the organizer will ALWAYS open a door that contains a goat" to draw the conclusion of the article. That knowledge is implicitly assumed. It's not implicitly assumed, it's stated in the original question: "You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat." You pick a door, the hosts opens another door which contains a goat. He can't open the door you chose, he can't open a door with the prize, he can't not open a door. Introducing a possibility which is not a part of the specified problem turns it into a different problem. > I have shown that by assuming a different knowledge - in this case, the organizer only opens the door that contains a goat when you choose the door that contains the car - you can end up with different probabilities. For every "the organizer only the opens a door that contains a goat when you choose the door that contains a car", there's an "the organizer only opens a door that contains a goat when you open a door that doesn't contain a car". Not knowing the host's behavior means that it isn't part of your analysis. If you don't know why he does what he does, all you can use are the facts in front of you: there are three doors, you pick one, you are shown a second door which doesn't contain the prize, and are offered a chance to choose. > I'm pretty certain that the probabilities in this problem are unknown unless you know the behavior of the organizer in EVERY situation, not in one particular case Not so. If you knew the host's behavior (which the original problem does specify precisely), you can use it in your analysis. But not knowing it, means the best decision has to be independent of it. And if you knew the door that contained the prize, you could use that in your analysis. But not knowing it, means the best decision has to be made independent of it.
  • ucha 12y ago
    You are making an assumption on the host behavior, the assumption being that if you repeat the experiment the host will open a door containing a goat. If you think you're not and that the 1/3 - 2/3 probabilities are correct based on the single observation you made, consider this: you have 1 black ball and a 2 white balls in 3 different urns each containing a ball. You select one urn A. Some external agent randomly overturns an urn. That ball it contains is white. What's the probability that the ball in urn A is black? The answer is 1/2. Not 1/3. It's 1/2 because you the assumption you make on the external agent's behavior is that it's random. If you don't make an assumption on its behavior, you can't calculate probabilities. If you make the assumption that the external agent picked up the white ball on purpose and will repeat that behavior when faced with similar circumstances, the probability is 2/3. My point is that if you don't make an assumption on the host's behavior, you can't calculate probabilities.