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My favourite probability problem

Posted By: Matt Cohn-Geier
Date: Friday, 28 August 2009, at 7:39 p.m.

In Response To: My favourite probability problem (Bob Koca)

It is perfectly acceptable to talk of the probability of an event that already occurred.

Acceptable but I really think in that case it is either 0 or 1.

Joe was asking about the probability of the envelope containing the million dollars and it definitely is important. Your non answer dodged the question. In Joe's case suppose that a fair coin was tossed and that if landed heads 40 times in a row that then the envelope would be left empty. At least one head and then the 1Million is put into it. That changes things doesn't it? Also would you still say it would be less than 1%?

The point here is that what the envelope contains depends on what the predictor thinks you will do. Specifically it will contain $1m if and only if the predictor predicts you will take only that envelope. It is not an independent event like a dice roll or a coin toss that doesn't depend in any way on you.

So asking what the odds are that the predictor will predict you to take only the envelope with $1m is unanswerable. There is no uniform answer. Saying "50%" or "<1%" would be directly answering the question but would be wrong.

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