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by movpasd
1026 days ago
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Thanks for the compliment about the bucket, I was quite pleased with it :) I do appreciate what you mean about the language issue — it's a misleading phrase that due to the context of the question encourages the listener to jump to "1/2". But it's quite a common expression in probability, and in that context the expression is unambiguous, if difficult to parse (like many things in mathematics, I suppose). |
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I agree that it's must be a standard understanding among statisticians that one of these interpretations is implied (although maybe given what happened with the Monty Hall problem, it's not really so standard?). It's legitimately interesting that these two different interpretations result in different answers, but I feel that it is rather confusing to tell an outsider of the field that 1/3 is "the" answer and that their intuitions are wrong -- when actually it's just one conventional interpretation.
The Monty Hall problem is often understated, and for example the "intuitive" answer of 1/2 (i.e. that switching doesn't matter) can be restored if we assume the host himself didn't know where the car was and just happened to reveal another mule by chance. The assumption that the host knows where the car is is often not mentioned explicitly. Now it's just convention that in other such scenarios that there should be a similar understanding.