Subject:
|
Re: math question (or pattern... whatever...)
|
Newsgroups:
|
lugnet.off-topic.geek
|
Date:
|
Tue, 4 Mar 2003 04:51:01 GMT
|
Viewed:
|
664 times
|
| |
|
|
On Tue, Mar 04, 2003 at 04:42:32AM +0000, David Eaton wrote:
> Actually, there's a 2/3 chance that it's behind door Z! A very sneaky
> problem, in fact. It was shown to us in high school as the subject of a very
> minor controversy. After being published as "2/3 chance" in a math
> publication, some college math professor (and his class) wrote in and said
> that it was in fact 1/2; which in turn inspired the magazine to further
> explain the answer :)
>
> The logic:
> In the initial pick, there's a 1/3 chance it's behind the door you picked;
> door X. And a 1/3 chance behind door Y, and another 1/3 for behind door Z.
> But, there's a *2/3* chance that it's behind EITHER Y or Z. And by showing
> you that it's *not* behind door Y, you know that if it *was* behind Y or Z
> (2/3 chance), that it's behind door Z. Hence, given that it's not behind
> door Y, the chance that it's behind door Z is 2/3.
I already proved that I should stay out of this... but. When you had 3
doors to pick from, it was 1/3 that whatever door you choose is the
correct one. However, after opening one of the doors you didn't pick
(assuming the host is not opening the door with the prize), it's like a
new question. Given two doors, pick one. One wins, one loses.
I always thought that probability has no memory. if you rolled a die 10
times, and got '1' in each roll... what's the chance of rolling a '1'
next time? 1/6 - there's no memory involved. However, if you say
"what's the chance of rolling 11 '1's in a row", that's a different
question.
Am I totally off base here?
--
Dan Boger
dan@peeron.com
|
|
Message has 1 Reply:
 | | Re: math question (or pattern... whatever...)
|
| (...) Nope. The analysis that I have seen that argues for a different outcome than 1/2 has to do with the fact that you're being (or so it is argued) conveyed more information than it seems. That is, they KNOW which door is right, and by showing you (...) (22 years ago, 4-Mar-03, to lugnet.off-topic.geek)
|
Message is in Reply To:
| | Re: math question (or pattern... whatever...)
|
| (...) Actually, there's a 2/3 chance that it's behind door Z! A very sneaky problem, in fact. It was shown to us in high school as the subject of a very minor controversy. After being published as "2/3 chance" in a math publication, some college (...) (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
|
|
|
|
