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kybernetikos comments on Probability is in the Mind - Less Wrong

60 Post author: Eliezer_Yudkowsky 12 March 2008 04:08AM

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Comment author: kybernetikos 21 November 2012 10:42:03PM *  3 points [-]

Thinking of probabilities as levels of uncertainty became very obvious to me when thinking about the Monty Hall problem. After the host has revealed that one of the three doors has a booby prize behind it, you're left with two doors, with a good prize behind one of them.

If someone walks into the room at that stage, and you tell them that there's a good prize behind one door and a booby prize behind another, they will say that it's a 50/50 chance of selecting the door with the prize behind it. They're right for themselves, however the person who had been in the room originally and selected a door knows more and therefore can assign different probabilities - i.e. 1/3 for the door they'd selected and 2/3 for the other door.

If you thought that the probabilites were 'out there' rather than descriptions of the state of knowledge of the individuals, you'd be very confused about how the probability of choosing correctly could at the same time be 2/3 and 1/2.

Considering the Monty Hall problem as a way for a part of the information in the hosts head to be communicated to the contestant becomes the most natural way of thinking about it.