Subject:
|
Re: math question (or pattern... whatever...)
|
Newsgroups:
|
lugnet.off-topic.geek
|
Date:
|
Tue, 4 Mar 2003 19:48:43 GMT
|
Viewed:
|
361 times
|
| |
|
|
In lugnet.off-topic.geek, Bruce Schlickbernd writes:
> I think your analysis is incorrect, precisely because you did *not* list all
> outcomes.
>
> Choose Prize Door Revealed Possible choices
> 1 1 2 Stay (win). Switch (lose).
> 1 1 3 Stay (win). Switch (lose).
> 1 2 3 Stay (lose). Switch (win).
> 1 3 2 Stay (lose). Switch (win).
>
> Choose Prize Door Revealed Possible choices
> 2 2 1 Stay (win). Switch (lose).
> 2 2 3 Stay (win). Switch (lose).
> 2 1 3 Stay (lose). Switch (win).
> 2 3 1 Stay (lose). Switch (win).
>
> Choose Prize Door Revealed Possible choices
> 3 3 1 Stay (win). Switch (lose).
> 3 3 2 Stay (win). Switch (lose).
> 3 1 2 Stay (lose). Switch (win).
> 3 2 1 Stay (lose). Switch (win).
>
> 12 different door combinations with 24 outcomes: 12 win if you stay, 12 win
> if you switch. The nine you list is very incomplete.
Actually, I explained (albeit briefly) why this isn't correct.
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:
> Choose Prize Door Revealed Possible choices
> 1 1 2 Stay (win). Switch (lose).
> 1 1 3 Stay (win). Switch (lose).
> 1 2 3 Stay (lose). Switch (win).
> 1 2 3 Stay (lose). Switch (win).
> 1 3 2 Stay (lose). Switch (win).
> 1 3 2 Stay (lose). Switch (win).
>
> Choose Prize Door Revealed Possible choices
> 2 2 1 Stay (win). Switch (lose).
> 2 2 3 Stay (win). Switch (lose).
> 2 1 3 Stay (lose). Switch (win).
> 2 1 3 Stay (lose). Switch (win).
> 2 3 1 Stay (lose). Switch (win).
> 2 3 1 Stay (lose). Switch (win).
>
> Choose Prize Door Revealed Possible choices
> 3 3 1 Stay (win). Switch (lose).
> 3 3 2 Stay (win). Switch (lose).
> 3 1 2 Stay (lose). Switch (win).
> 3 1 2 Stay (lose). Switch (win).
> 3 2 1 Stay (lose). Switch (win).
> 3 2 1 Stay (lose). Switch (win).
In essense, the thing that's actually contributing to the permutation is the
choice you made and where the prize is. Which door specifically is revealed
is irrelevant to the permutation, since EITHER way the door is chosen, the
outcome is the same (effectively, it's a sub-permutation).
Regardless, because we *know* that the host *always* obeys certain rules (IE
he'll always reveal a goat-door that you didn't pick), we can equivalently
say that he always picks the lowest-numbered doors to reveal in case of a
tie, since he's ALREADY using an algorithm.
If you're still not getting it, seriously-- try it yourself. Try with
keeping your original choice a bunch of times, then try with switching a
bunch of times. Actually, I believe Larry posted a site with links to
simulators (not that I tried them) where you can play with it as much as you
want.
DaveE
|
|
Message has 2 Replies:
 | | Re: math question (or pattern... whatever...)
|
| (...) 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 - (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
| | | Re: math question (or pattern... whatever...)
|
| (...) Whew. You are way off in your probablity and statistics analysis: if you want to double everything, then you would have to list 112 and 113 twice also. They are *not* the same selection. (...) and 1 1 2 (...) and 1 1 3 (...) (etc. snip) (...) (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
|
Message is in Reply To:
| | Re: math question (or pattern... whatever...)
|
| (...) I think your analysis is incorrect, precisely because you did *not* list all outcomes. Choose Prize Door Revealed Possible choices 1 1 2 Stay (win). Switch (lose). 1 1 3 Stay (win). Switch (lose). 1 2 3 Stay (lose). Switch (win). 1 3 2 Stay (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
|
61 Messages in This Thread:
 
 
- Entire Thread on One Page:
- Nested:
All | Brief | Compact | Dots
Linear:
All | Brief | Compact
This Message and its Replies on One Page:
- Nested:
All | Brief | Compact | Dots
Linear:
All | Brief | Compact
|
|
|
|
