|
|
Joined: May 2002
Posts: 1,529
veteran
|
OP
veteran
Joined: May 2002
Posts: 1,529 |
Three closed doors are numbered 1, 2, and 3.
Behind one door is the nice behind of Vanna White who sits on a stool smilling. You like her.
Behind the other two doors are bags of Jim Dandy dog food. You don't have a dog.
You can have what is behind the door you select...so select.
Nice choice. But before openning the door that you have selected, Monty Hall opens one of the other doors and shows you a sack of Jim Dandy dog food and asks you if you would now like to change your first selection.
You should.
Why?
|
|
|
|
|
Joined: Sep 2000
Posts: 2,891
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Sep 2000
Posts: 2,891 |
I remember having this explained to me once, but even after the explanation - it still did not make sense to me (no matter how much the guy was convinced it did.)
|
|
|
|
|
Joined: Jul 2000
Posts: 3,467
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Jul 2000
Posts: 3,467 |
I think we've already beaten this one to death, with several people concluding that in spite of the overwhelming mathematical evidence that a switch will give you a 2-1 edge they choose not to believe the correct conclusion. To see the solution discussed at length, along with several programs that prove the 2-1 edge, see the Monte Hall Problem at wikipedia.com.
TEd
|
|
|
|
|
Joined: May 2002
Posts: 1,529
veteran
|
|
OP
veteran
Joined: May 2002
Posts: 1,529 |
Quote:
I think we've already beaten this one to death, with several people concluding that in spite of the overwhelming mathematical evidence that a switch will give you a 2-1 edge they choose not to believe the correct conclusion. To see the solution discussed at length, along with several programs that prove the 2-1 edge, see the Monte Hall Problem at wikipedia.com.
Thank you Ted.
But your summary mainly points out your disinterest and not the continuing interest of others -- me, for example.
What I want to demostrate is a point beyond the points made three years ago. And if you become interested at that point then you are certainly welcome to put your opinions back into this thread.
|
|
|
|
|
Joined: Dec 2000
Posts: 13,803
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Dec 2000
Posts: 13,803 |
Quote:
Why?
Because you now have a 2 to 1 chance of picking the right door. If you chose the wrong door in the first guess (a 2 to 1 chance) by changing you will get the right door.
Now, my dear Christmas turkey, what is your hidden agenda?
|
|
|
|
|
Joined: May 2002
Posts: 1,529
veteran
|
|
OP
veteran
Joined: May 2002
Posts: 1,529 |
Quote:
Quote:
Why?
Because you now have a 2 to 1 chance of picking the right door. If you chose the wrong door in the first guess (a 2 to 1 chance) by changing you will get the right door.
Now, my dear Christmas turkey, what is your hidden agenda?
No Faldage, little grasshopper; you did not count properly. After changing your pick you will not automatically "get the right door" then you will only have a two-third chance of picking the right door.
Go now and study. Return here when total understanding becomes your handmaiden; and then and only then will I reveal the secret understanding.
Last edited by themilum; 11/05/06 08:36 PM.
|
|
|
|
|
Joined: Oct 2006
Posts: 293
enthusiast
|
|
enthusiast
Joined: Oct 2006
Posts: 293 |
The overwhelming (to me, at least) paradox of "the laws of chance" dictate that on each selection you have an equal chance of making the correct (or incorrect) choice.
I see the logic involved in changing from 1 out of 3 to 50%.
But I always remember:
We know by the "laws" of chance, if you were to flip a coin in the air 1000 times; about 500 times it will land on tails.
However, it is entirely possible that flip # 300 through 500 are ALL heads.
Pondering this always causes me a headache !!
--------------------
"I am certain there is too much certainty in the world" -Michael Crichton
|
|
|
|
|
Joined: May 2002
Posts: 1,529
veteran
|
|
OP
veteran
Joined: May 2002
Posts: 1,529 |
But ParkinT, you missed the point.
By a oddity of mathematics the switch in doors gives the participant not a one-in-two (50%) even chance, but a two-thirds (66.6%) advandage in correctly selecting the right door.
I've checked it out myself and it can be proven by random number applications.
Strange.
|
|
|
|
|
Joined: Dec 2000
Posts: 13,803
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Dec 2000
Posts: 13,803 |
Quote:
Quote:
Quote:
Why?
Because you now have a 2 to 1 chance of picking the right door. If you chose the wrong door in the first guess (a 2 to 1 chance) by changing you will get the right door.
Now, my dear Christmas turkey, what is your hidden agenda?
No Faldage, little grasshopper; you did not count properly. After changing your pick you will not automatically "get the right door" then you will only have a two-third chance of picking the right door.
Go now and study. Return here when total understanding becomes your handmaiden; and then and only then will I reveal the secret understanding.
Perhaps you didn't read my post with sufficient care. What I said was:
Quote:
If you chose the wrong door in the first guess (a 2 to 1 chance) by changing you will get the right door. (emphasis added)
which looks to me like the very thing you accuse me of not saying. So you can take your stuffing and drop it off in that little house out back.
Now, what's your point?
|
|
|
|
|
Joined: Dec 2000
Posts: 13,803
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Dec 2000
Posts: 13,803 |
Quote:
The overwhelming (to me, at least) paradox of "the laws of chance" dictate that on each selection you have an equal chance of making the correct (or incorrect) choice.
I see the logic involved in changing from 1 out of 3 to 50%.
Let's try this little thought experiment:
We have three cards. An ace and two deuces. I shuffle the cards around and lay them out on the table. You choose one card that you think is the ace. What are your chances of being right?
If you said 1 in 3, congratulations, you're correct.
Now, I (knowing which card is the ace, because I peeked) touch one of the other two cards. What are your chances of having selected the ace on your first try?
If you said 1 in 3, congratulations. Nothing has changed, so your chances are still the same.
Now, I turn that card over, showing a deuce. What are your chances of having been correct on your first try?
If you said 1 in 2, please explain what has changed. Remember, I can always turn over a deuce. If you said 1 in 3, congratulations. Nothing has changed except you now know that one of the cards you didn't choose was a deuce. The chances of your first guess being correct are still 1 in 3. If you have two cards to choose from and one of them has a 1 in 3 chance of being the ace, what are the chances of the other being an ace?
The answer is left as an exercise for the student.
|
|
|
|
Forums16
Topics13,913
Posts229,342
Members9,182
| |
Most Online3,341
Dec 9th, 2011
|
|
|
0 members (),
491
guests, and
1
robot. |
|
Key:
Admin,
Global Mod,
Mod
|
|
|
|
