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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Mon, 3 Mar 2003 21:46:31 GMT
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Viewed:
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304 times
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In lugnet.off-topic.geek, David Koudys writes:
> In lugnet.off-topic.geek, Adrian Drake writes:
> > In lugnet.off-topic.geek, David Koudys writes:
> > > k, here's something that came across my desk...
> > >
> > > you have a bag with 4 marbles in it.
> > >
> > > 2 of the marbles are red
> > > 1 marble is white
> > > 1 marble is blue
> > >
> > > you reach in and grab 2 random marbles
> > >
> > > you open up your hand a bit to only see the colour of one of those 2
> > > marbles, and it happens to be red
> > >
> > > what is the chance that the other marble in your hand is also red?
> > >
> > > I say it's 33 percent
> > > my friend says it's 20 percent
> >
> > <long snip>
> >
> > you're right, in both senses. Your logic for the first solution is valid,
> > and your identification of his error in the second solution (which would
> > lead to the same answer) is also correct. It is, indeed, 33%
> >
> > Adrian
> > --
> > http://www.brickfrenzy.com
>
> Thanks for the support.
>
> Here's his rationale, hopefully explained more fully (but I still think it's
> not quite kosher...)
>
> The time of the event--you grabbed 2 marbles
>
> there are 6 possible combinations in your hand
>
> r(1) r(2)
> r(1) b
> r(1) w
> r(2) b
> r(2) w
> b w
>
> those are the 6 unique possibilities in your hand at the time of the event
>
> One of those possibilities becomes invalidated because as soon as we see one
> of the marbles, we know it's red so the b w is gone...
>
> thus leaving only 5 possibilities, and what we want is the chance that both
> marbles are red, from the event--
>
> 1 in 5, = 20 percent.
>
> I understand it, but it still isn't sitting right with me.
I think he's wrong because he's trying to reason about partial knowledge,
and that always causes problems. Look at it as a draw without replacement
instead. The order you reveal things doesn't influence outcomes, they were
what they were.
you drew two marbles, you looked at one. But when you drew the second marble
it was a draw without replacement from the bag. You could have drawn,
looked, drawn or drawn, drawn, looked and it's (in this case) logically
equivalent.
Think of it this way... you drew a marble. there are three left in the bag
to draw. If the first marble is red, the three left to draw are one of each.
So the chance that the second marble is red is 1 in 3. It doesn't in this
case change what marbles were in the bag because you waited to look at the
first one. IMHO. (1)
1 - But then I failed statistics the first time I took it. (2)
2 - However that was also the semester I got engaged, I never actually went
to class, did homework or took any tests except the final.
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Message has 1 Reply:
 | | Re: math question (or pattern... whatever...)
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| In lugnet.off-topic.geek, Larry Pieniazek writes: <snip> (...) Thanks Larry, I'll add it to the rationale. I failed gr. 12 advanced math once--was too busy being the editor of the yearbook that particular year (and playing cards in the cafeteria) It (...) (22 years ago, 3-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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| (...) Here's his rationale, hopefully explained more fully (but I still think it's not quite kosher...) The time of the event--you grabbed 2 marbles there are 6 possible combinations in your hand r(1) r(2) r(1) b r(1) w r(2) b r(2) w b w those are (...) (22 years ago, 3-Mar-03, to lugnet.off-topic.geek)
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