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 04:42:32 GMT
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Viewed:
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311 times
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In lugnet.off-topic.geek, David Koudys writes:
> In lugnet.off-topic.geek, David Eaton writes:
> > Now, here's a trickier one:
> >
> > Ever watched the old game show "Let's Make a Deal"? Sometimes, they'd offer
> > people things similar to this scenario. You're a game show contestant. Bob
> > the host shows you 3 doors. You win whatever's behind the door you pick.
> > Behind 2 of the doors are goats. Behind the other door, there's a brand new
> > sports car.
> >
> > You pick door X. Now, before Bob shows you what's behind door X, he opens up
> > door Y, and shows you... a goat! Bob now says you have a chance to change
> > your mind, and instead of picking door X, you can switch to door Z.
> >
> > What's the probability that the sports car is behind door Z versus door X?
> >
> > DaveE
>
> I'd say 1 in 2, or 50 percent, but maybe I'm missing something.
>
> Good question though.
Actually, there's a 2/3 chance that it's behind door Z! A very sneaky
problem, in fact. It was shown to us in high school as the subject of a very
minor controversy. After being published as "2/3 chance" in a math
publication, some college math professor (and his class) wrote in and said
that it was in fact 1/2; which in turn inspired the magazine to further
explain the answer :)
The logic:
In the initial pick, there's a 1/3 chance it's behind the door you picked;
door X. And a 1/3 chance behind door Y, and another 1/3 for behind door Z.
But, there's a *2/3* chance that it's behind EITHER Y or Z. And by showing
you that it's *not* behind door Y, you know that if it *was* behind Y or Z
(2/3 chance), that it's behind door Z. Hence, given that it's not behind
door Y, the chance that it's behind door Z is 2/3.
Think about it this way:
If there were 1,000,000 doors instead of 3, and you picked door #1. Now,
suddenly, the host opens 999,998 of the remainging doors and shows you
they're all full of goats, EXCEPT for door #821,744 (which he doesn't show
you). Given the odds of you happening to choose the magic door on your first
guess, I think it's fair to say you'd change doors pretty quick! (Unless
maybe you prefer goats!)
DaveE
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Message has 2 Replies:
 | | Re: math question (or pattern... whatever...)
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| (...) I already proved that I should stay out of this... but. When you had 3 doors to pick from, it was 1/3 that whatever door you choose is the correct one. However, after opening one of the doors you didn't pick (assuming the host is not opening (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
| | | Re: math question (or pattern... whatever...)
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| (...) Inasmuch as you get to pick a second time, the odds are 50/50. If you did not get to pick a second time, the odds would be 1/3, not 1/2. Of course, this is leaving out the poker aspect: if your initial pick was incorrect, would they even offer (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
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