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 21:16:03 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, Larry Pieniazek writes:
> > In lugnet.off-topic.geek, David Koudys writes:
> >
> > > I still like the 50 percent possibility tho.
> >
> > Liking it or not is irrelevant. The probabilities are what they are.
> >
> > And the answer is still 2/3 if you switch, given the premises. No matter
> > whether you like it or not.
> >
> > Go to the site I gave you and read what is written there.
>
> Got it...
>
> Goes into a fairly comprehensible walk-thru, but the point that makes it
> obvious (as stated) is:
>
> "
> Imagine that there were a million doors. Also, after you have chosen your
> door; Monty opens all but one of the remaining doors, showing you that they
> are "losers." It's obvious that your first choice is wildly unlikely to have
> been right. And isn't it obvious that of the other 999,999 doors that you
> didn't choose; the one that he didn't open is wildly likely to be the one
> with the prize?
> "
>
> I like it.
>
> I renounce my 50/50
>
> Dave K
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!
Leaving---
hand left in bag
r1 w
w r1
Not swapping--50/50
Swapping (obviously) 50/50
Now let's change the story--there are 4 balls in the bag, one is white, the
rest are red...
You are told to grab one and not look--chances that it's white, 1 in 4, or
25 percent
hand in bag
r1 r2 r3 w
r2 r1 r3 w
r3 r1 r2 w
w r1 r2 r3 winner!
Now I remove 1 red from the bag, and give you the option to switch (again,
lets say the last red)
hand in bag
r1 r2 *r3* w
r2 r1 *r3* w
*r3* r1 r2 w - read above--cannot be a possibility
w r1 r2 *r3*
Leaving
hand in bag
r1 r2 w
r2 r1 w
w r1 r2 Winner
1 in 3, or 33 percent--for not swapping--swapping is still 33 percent
So I'd say logically, if you continue this out to 'You have 1000 balls in a
bag, 999 are red and 1 is white, the chances of you picking the white one
right out of the bag is 1 in 1000
If I remove a red ball from the bag, you're chances are now 1 in 998 that
you have the white one, and if you swap, it's still 1 in 998
I think--this is fun to wrap my mind around...
Dave K
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Message has 1 Reply:
 | | Re: math question (or pattern... whatever...)
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| (...) 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 (...) (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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| (...) Got it... Goes into a fairly comprehensible walk-thru, but the point that makes it obvious (as stated) is: " Imagine that there were a million doors. Also, after you have chosen your door; Monty opens all but one of the remaining doors, (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
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