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 22:08:08 GMT
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Viewed:
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451 times
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In lugnet.off-topic.geek, David Koudys writes:
> In lugnet.off-topic.geek, James Brown writes:
> > In lugnet.off-topic.geek, David Koudys writes:
> > >
> > > I think I may have found the fallacy...
> > > (indulge me if you please)
> > >
> > > Here's a bag with 3 marbles in it--2 are red (goats, whatever), one is white
> > > (brand new car)
> > >
> > > Pick a random one out of the bag and hold it in your hand--don't look at it!
> > > What's the chances that it's white (the winner)?
> > >
> > > hand left in bag
> > > r1 r2 w
> > > r2 r1 w
> > > w r1 r2 Winner!
> > >
> > > I think we all agree it's 33 percent.
> > >
> > > Now I'm going to take a red one out of the bag, so there's only one marble
> > > left in the bag--now you have a choice to keep the marble in your hand, or
> > > swap it for the one in the bag--
> > >
> > > What are the results?
> > >
> > > First, one red is eliminated--
> > > hand left in bag
> > > r1 *r2* w
> > > *r2* r1 w -cannot be a possibility for r2 is pulled out of the bag
> > > w r1 *r2* Winner!
> >
> > Nope, you're assuming that the marble pulled out of the bag is r2. It might
> > be r1. Better to leave off the numbers, as the red marbles are not distinct.
> >
> > hand bag
> > r r w
> > r r w
> > w r r
> >
> > remove a red from the bag and it reduces to:
> >
> > hand bag
> > r w
> > r w
> > w r
> >
> > Clear as mud? ;)
> >
> > James
>
> Clear as mud, for then if the red is irrelevant, then there cannot be
>
> > hand bag
> > r w
> > r w
> > w r
>
> there can only be
>
> > hand bag
> > r w
> > w r
>
> for if we remove either red ball from the bag, that very same red ball in
> this specific instance cannot be in the person's hand. We cannot take a
> ball out of the bag and in the same example say it may be one of the options
> in the person's hand.
Why not? There are two different red balls, so each of those red balls is
equally likely as the white ball to be in my hand.
> If the red *is* relevant, then we're back to my hypothesis, as posted above.
No, because you only tried to remove r2. We are only removing *a* red ball
from the bag; because there are 2 red balls, and only 1 is ever in our hand,
there is always a red ball in the bag to remove. It is irrelevant whether
that ball is r1 or r2.
Redoing it with numbers:
hand bag
r1 r2 w
r2 r1 w
w r1 r2
Now removing a red ball from the bag we get:
hand bag
r1 w (r2 is the only red ball, it is removed)
r2 w (r2 is the only red ball, it is removed)
w r1 OR r2 (either may be removed, as both are in the bag)
James
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Message has 2 Replies:
 | | Re: math question (or pattern... whatever...)
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| (...) This analysis assumes there is a percievable difference between the red balls, which as originally stated, there isn't. It's similar to the difference between combinations and permutations. The two permutations you've listed with a red ball in (...) (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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| (...) Clear as mud, for then if the red is irrelevant, then there cannot be (...) there can only be (...) for if we remove either red ball from the bag, that very same red ball in this specific instance cannot be in the person's hand. We cannot take (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
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