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* * * * - 2 votes

Million Dollar Urns


Best Answer superprismatic, 07 October 2013 - 03:03 PM

Spoiler for what I would pay to play

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16 replies to this topic

#1 BMAD

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Posted 04 October 2013 - 07:20 PM

One million dollar coins are thrown into two urns in the following manner: At the beginning of the process, each urn contains one coin.  The remaining 999,998 coins are thrown in one by one.  Each coin lands into one of the two urns with different probabilities.  If at any stage of the process the first urn contains x coins and the second urn contains y coins, then the probabilities that the thrown coin will fall into the first or second urn are:

 

x/(x+y) and y/(x+y)

 

The question is: how much should you pay (in advance) for the contents of the urn that contains the smaller amount of coins?


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#2 phil1882

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Posted 04 October 2013 - 09:43 PM

Spoiler for

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#3 BMAD

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Posted 05 October 2013 - 03:59 PM

lol, yes.  I mean 1 million, $1 coins.  verify the solution


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#4 phil1882

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Posted 05 October 2013 - 04:57 PM

Spoiler for small case

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#5 superprismatic

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Posted 05 October 2013 - 10:41 PM

Spoiler for derivation


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#6 plasmid

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Posted 06 October 2013 - 05:08 AM

Spoiler for Can you do recursions like that?

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#7 superprismatic

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Posted 06 October 2013 - 03:43 PM

Spoiler for Can you do recursions like that?

Spoiler for sorry, my mistake


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#8 superprismatic

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Posted 07 October 2013 - 03:03 PM   Best Answer

Spoiler for what I would pay to play


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#9 DeGe

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Posted 08 October 2013 - 01:16 PM

Spoiler for Explanation for a quarter


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#10 bonanova

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Posted 09 October 2013 - 09:51 PM

One million dollar coins are thrown into two urns in the following manner: At the beginning of the process, each urn contains one coin.  The remaining 999,998 coins are thrown in one by one.  Each coin lands into one of the two urns with different probabilities.  If at any stage of the process the first urn contains x coins and the second urn contains y coins, then the probabilities that the thrown coin will fall into the first or second urn are:

 

x/(x+y) and y/(x+y)

 

The question is: how much should you pay (in advance) for the contents of the urn that contains the smaller amount of coins?

 

Spoiler for cute problem


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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