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 20:38:13 GMT
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Viewed:
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378 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:
> > > You see, you now have 2 listings for "Choose 1, Prize 1", "Coose 2, Prize
> > > 2", and "Choose 3, Prize 3", when each deserves *equal* probability to each
> > > other possibility, like "Choose 2, Prize 3"-- which in your list, only gets
> > > one entry. Basically, if you want to count "Choose 1, Prize 1, Door Revealed
> > > 2" and "Choose 1, Prize 1, Door Revealed 3" as *different*, then you have to
> > > count each *other* selection twice as well, resulting in:
> >
> > That doesn't make sense at all--
> >
> > If I choose door 1 and the prize is behind door 1, the host can choose to
> > show me door 2 *or* door 3 - 2 possibilities
> >
> > If I choose door one and the prize is behind door 2, the host can *only*
> > show me door 3 - one possibility
> >
> > If I choose door one and the prize is behind door 3, the host can *only*
> > show me door 2 - one possibility
> >
> > So if I choose door 1, there are only 4 possibilities, not 6, as you listed
> > below.
> >
> > Now whether I switch or stay, as listed above, is 50/50
>
> Doh. This is just coming back to haunt me. I should never have included the
> "door revealed" column. It's entirely irrelevant, and is only serving to
> confuse. A better list:
>
> Prize Choice Switch or Stay?
> 1 1 stay!
> 1 2 switch!
> 1 3 switch!
> 2 1 switch!
> 2 2 stay!
> 2 3 switch!
> 3 1 switch!
> 3 2 switch!
> 3 3 stay!
If I were to think about it like a sequence of events, logically leading up
to the end choice, it would go something like this--
The event starts--
Contestant picks a door -- 1, 2, or 3
If this is all there is to the contest, we have 33 percent chance of picking
the right door, as posted above (listed here for clarity)
Door Prize Win/Lose
1 1 win!
1 2 lose!
1 3 lose!
2 1 lose!
2 2 win!
2 3 lose!
3 1 lose!
3 2 lose!
3 3 win!
3 wins, 6 losses--33 percent
But this isn't where we put the stake in the ground...
The event continues--
One door, which isn't my picked door or the prize door, is revealed,
hypothetically, let's say door number 3
So anything with a 3 in it cannot be a choice, for it is eliminated--
Door Prize Win/Lose
1 1 win!
1 2 lose!
1 3 lose! *delete me*
2 1 lose!
2 2 win!
2 3 lose! *delete me*
3 1 lose! *delete me*
3 2 lose! *delete me*
3 3 win! *delete me*
Leaving--
Door Prize Win/Lose
1 1 win!
1 2 lose!
2 1 lose!
2 2 win!
So here's the stake in the ground--the end of the event--I must choose
between 2 doors--the one I originally wanted, or the other door remaining...
And, it's 50/50...
k, now I'm just more confus-ed... :)
Dave K
> Effectively, there's a 1/3 chance that the prize is in door #1. And there's
> a 1/9 chance that you *PICK* door number 1 AND that the prize is back there.
> Further, there's a 1/18 chance that it's Prize 1, Choice 1, door revealed 2,
> and another 1/18 chance that it's Prize 1, Choice 2, door revealed 3.
>
> HOWEVER. It's a 1/3 chance that the prize is in door #1. 1/9 chance that you
> pick door #2. And since there's only ONE choice of doors to be revealed,
> it's a 1/9 chance that it's Prize 1, Choice 2, door revealed 3.
>
> Hence, probability wise (using Bruce's model):
>
> Prob. Choose Prize Door Revealed Possible choices
> 1/18 1 1 2 Stay (win). Switch (lose).
> 1/18 1 1 3 Stay (win). Switch (lose).
> 1/9 1 2 3 Stay (lose). Switch (win).
> 1/9 1 3 2 Stay (lose). Switch (win).
>
> Prob. Choose Prize Door Revealed Possible choices
> 1/18 2 2 1 Stay (win). Switch (lose).
> 1/18 2 2 3 Stay (win). Switch (lose).
> 1/9 2 1 3 Stay (lose). Switch (win).
> 1/9 2 3 1 Stay (lose). Switch (win).
>
> Prob. Choose Prize Door Revealed Possible choices
> 1/18 3 3 1 Stay (win). Switch (lose).
> 1/18 3 3 2 Stay (win). Switch (lose).
> 1/9 3 1 2 Stay (lose). Switch (win).
> 1/9 3 2 1 Stay (lose). Switch (win).
>
> DaveE
Dave K
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Message is in Reply To:
 | | Re: math question (or pattern... whatever...)
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| (...) Doh. This is just coming back to haunt me. I should never have included the "door revealed" column. It's entirely irrelevant, and is only serving to confuse. A better list: Prize Choice Switch or Stay? 1 1 stay! 1 2 switch! 1 3 switch! 2 1 (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
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