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 18:48:31 GMT
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Viewed:
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350 times
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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.
-->Bruce<--
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Message has 3 Replies:
 | | Re: math question (or pattern... whatever...)
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| In lugnet.off-topic.geek, Bruce Schlickbernd writes: <snip> (...) So, like others suggest about knowing that one of the marbles is red, the chance that the other one is red... the one that we know becomes basically irrelevant to the chance--there (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
| | | Re: math question (or pattern... whatever...)
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| (...) 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 (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
| | | Re: math question (or pattern... whatever...)
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| (...) Actually, I explained (albeit briefly) why this isn't correct. You see, you now have 2 listings for "Choose 1, Prize 1", "Coose 2, Prize 2", and "Choose 3, Prize 3", when each deserves *equal* probability to each other possibility, like (...) (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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| (...) 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 (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
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