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 06:16:11 GMT
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Viewed:
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324 times
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In lugnet.off-topic.geek, David Eaton writes:
> 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 :)
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 the second chance? In fact, they did, but what
percentage of the time I couldn't tell you, but I would suspect that they
decided on showing a wrong door no matter what as part of the script (take X
long to make a presentation).
>
> 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.
They can *always* show you a door that the car is not behind. It doesn't
improve your chances at all if there is no second chance to pick. What you
are saying is that it is *always* a 2/3 chance that you are right.
-->Bruce<--
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Message has 2 Replies:
 | | Re: math question (or pattern... whatever...)
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| (...) See the link I posted and follow some of the links it has. You are in good company, lots of mathemeticians came to the same conclusion. (and roasted Marilyn Vos Savant about it at the time it first got a lot of publicity) That was before they (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
| | | 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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Message is in Reply To:
| | Re: math question (or pattern... whatever...)
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| (...) 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 (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
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