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Topic: A good probability puzzle but what is the right wording?
Replies: 10   Last Post: Feb 24, 2013 12:19 PM

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David Petry

Posts: 1,103
Registered: 12/8/04
Re: A good probability puzzle but what is the right wording?
Posted: Feb 5, 2013 8:01 PM
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On Tuesday, February 5, 2013 7:15:50 AM UTC-8, Paul wrote:
> On Tuesday, February 5, 2013 4:10:33 AM UTC, Ray Vickson wrote:
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> > A variant I prefer is one that made the rounds of the Operations Research community some years ago.
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> > You are presented with two opaque bags, and are told that one bag contains twice as much money as the other. You are allowed to open one bag before choosing your prize bag. If you open one of the bags and see $10, should you switch to the other bag?
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> > One popular argument at the time was that the other bag contains either $5 or $20, with equal probabilities, and since the expected value is $25/2 = $12.50 > $10, then yes, you should switch.
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> > However, this seems fishy, since the same type of argument would apply to any opened bag.
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> > RGV
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> You stick with the $10 bag because academics aren't generous enough with cash to risk giving away as much as $20.
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> On a more serious note, this is a case of no-solution-because-of-unspecified-probability-distribution -- the two envelopes problem.
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> It's too different from the original question to qualify as a "variant".
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> Paul Epstein


If the question is changed ever so slightly, then it is almost exactly the same problem: is there a strategy you can use to have greater than even odds that you pick the bag with more money?






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