Subject:
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Re: math question (or pattern... whatever...)
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Newsgroups:
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lugnet.off-topic.geek
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Date:
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Tue, 4 Mar 2003 19:46:47 GMT
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Viewed:
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364 times
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In lugnet.off-topic.geek, Bruce Schlickbernd writes:
> In lugnet.off-topic.geek, David Eaton writes:
>
> > For any still not getting this one (it's tricky!) here's another way to
> > analyze the problem. List all outcomes:
> >
> > Prize Choice Door Revealed Stay or Switch?
> > 1 1 2 stay!
> > 1 2 3 switch!
> > 1 3 2 switch!
> > 2 1 3 switch!
> > 2 2 1 stay!
> > 2 3 1 switch!
> > 3 1 2 switch!
> > 3 2 1 switch!
> > 3 3 1 stay!
> >
> > Notice that only 1/3 of the time would you win by sticking with your
> > original door. The other 2/3 of the time, you win by switching.
>
> I think your analysis is incorrect, precisely because you did *not* list all
> outcomes.
>
> Choose Prize Door Revealed Possible choices
> 1 1 2 Stay (win). Switch (lose).
> 1 1 3 Stay (win). Switch (lose).
> 1 2 3 Stay (lose). Switch (win).
> 1 3 2 Stay (lose). Switch (win).
>
> Choose Prize Door Revealed Possible choices
> 2 2 1 Stay (win). Switch (lose).
> 2 2 3 Stay (win). Switch (lose).
> 2 1 3 Stay (lose). Switch (win).
> 2 3 1 Stay (lose). Switch (win).
>
> Choose Prize Door Revealed Possible choices
> 3 3 1 Stay (win). Switch (lose).
> 3 3 2 Stay (win). Switch (lose).
> 3 1 2 Stay (lose). Switch (win).
> 3 2 1 Stay (lose). Switch (win).
>
> 12 different door combinations with 24 outcomes: 12 win if you stay, 12 win
> if you switch. The nine you list is very incomplete.
You're also being incompletely rigorous. :) If you want to do an "all
possible outcomes" probability check, you have to add in all the 'door
revealed=prize' options which exist for the sake of the probabilities
involved, but are never invoked because the host will never show you the
winning door. It's been very thoroughly examined - the odds are 2/3. Check
out the links in this thread, some of which have simulation programs to
calculate the odds the long way for you.
James
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Message has 1 Reply:
 | | Re: math question (or pattern... whatever...)
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| (...) Which is why those are left out: there never enter the scenario. Only those that would actually happen are "invoked". And the simulator supports my conclusions. Only if the host "cheats" does the 2/3 option become statistically correct. :-) (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
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Message is in Reply To:
| | Re: math question (or pattern... whatever...)
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| (...) I think your analysis is incorrect, precisely because you did *not* list all outcomes. Choose Prize Door Revealed Possible choices 1 1 2 Stay (win). Switch (lose). 1 1 3 Stay (win). Switch (lose). 1 2 3 Stay (lose). Switch (win). 1 3 2 Stay (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
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