FWIW!! Whoops!
 

Eisboch wrote:

"Wizard of Woodstock" wrote in message
...


Math illiteracy affects 8 out of every 5 people.


Speaking of math illiteracy.

My son, also bored with winter, hit me with this classic "Monty Hall"
challenge last night.
Goes something like:

=================================================

A contestant is on "Let's Make a Deal". She is told that behind one of
three curtains there is a new car. Behind the other two curtains are
dirty old goats.

She picks a curtain. Before it is opened, one of the other curtains is
opened to reveal some dirty old goats.

She is then given the opportunity to change her mind about which
remaining curtain she thinks the car is behind.

What should she do?

================================================

Surprisingly, I chose what is considered to be the correct answer.
I'll let those that have never heard of this think about it and decide
for themselves.

Eisboch

Pick the curtain she did not choose

--

Looking to for a good time?

click here to make yourself feel good.

http://tinyurl.com/d3vxvm

FWIW!! Whoops!
 

"Wizard of Woodstock" wrote in message
...
On Thu, 29 Jan 2009 12:21:07 -0500, "Reginald P. Smithers III, Esq."
wrote:

John H wrote:
On Thu, 29 Jan 2009 08:55:42 -0800 (PST), wrote:

On Jan 29, 11:58 am, John H wrote:
On Thu, 29 Jan 2009 10:29:16 -0500, "Reginald P. Smithers III, Esq."

wrote:
John H wrote:
Make that $200 I'm in the hole for already.
Thanks again y'all
I'm getting phone calls, "Dad, do you know who (various) is?" He
made a
donation and I don't know him!" She's thrilled.
--
John H
* The original point and click interface was a Smith & Wesson. *
You really do need to include the link in your sig file.
Great idea! Let's see if this works...

--
John H

Go here first...http://tinyurl.com/d3vxvm

* Definition of a teenager?
God's punishment...for enjoying sex. *
Yup, nice hat by the way! Sure looks like a happy family!

Must have been the stuff in the ice cream!
--
John H

Go here first... http://tinyurl.com/d3vxvm

* Definition of a teenager?
God's punishment...for enjoying sex. *

Damn nice hat, where did you find such a good hat?

That hat sucks - for yuppie dorks.

Or retired Army dorks.

Real men wear Barmah Bush hats.

Pansey.

--

If we aren't supposed to eat animals,
why are they made of meat?

Nice had. Lots of shade. Those of us that are pigment challenged need
those big hats.

FWIW!! Whoops!
 

On Thu, 29 Jan 2009 20:29:09 GMT, Wizard of Woodstock
wrote:

On Thu, 29 Jan 2009 15:14:05 -0500, "Eisboch"
wrote:


"Wizard of Woodstock" wrote in message
. ..


Math illiteracy affects 8 out of every 5 people.


Speaking of math illiteracy.

My son, also bored with winter, hit me with this classic "Monty Hall"
challenge last night.
Goes something like:

================================================ =

A contestant is on "Let's Make a Deal". She is told that behind one of
three curtains there is a new car. Behind the other two curtains are dirty
old goats.

She picks a curtain. Before it is opened, one of the other curtains is
opened to reveal some dirty old goats.

She is then given the opportunity to change her mind about which remaining
curtain she thinks the car is behind.

What should she do?

============================================== ==

Surprisingly, I chose what is considered to be the correct answer.
I'll let those that have never heard of this think about it and decide for
themselves.

It's simple. There are two doors left which leaves three choices. Of
the three choices, two probabilities exist that she wins the car by
switching her choice.

She switches her choice to increase the probability of winning the
car.

Doesn't make sense.
She made her choice when the odds were 2:1 against her.
Since one curtain was eliminated, the odds are now 1:1.
Changing her choice won't change the odds.
The odds changed when the first curtain was opened.
Flip a coin 10 times and it comes up heads each time.
What are the odds of heads on the 11th flip?
Same as they were on the first flip. 1:1.
Or even money for you real gamblers.
Of which Galactic guys don't qualify.
Unless you're wagering quateros on warpsnerk lightbeam racing.

--Vic

FWIW!! Whoops!
 

On Jan 29, 10:53*pm, Vic Smith
Unless you're wagering quateros on warpsnerk lightbeam racing.

--Vic

Tribbles, man... bet with TRIBBLES!

FWIW!! Whoops!
 

"Vic Smith" wrote in message
...
On Thu, 29 Jan 2009 20:29:09 GMT, Wizard of Woodstock
wrote:

On Thu, 29 Jan 2009 15:14:05 -0500, "Eisboch"
wrote:


"Wizard of Woodstock" wrote in message
...


Math illiteracy affects 8 out of every 5 people.


Speaking of math illiteracy.

My son, also bored with winter, hit me with this classic "Monty Hall"
challenge last night.
Goes something like:

=============================================== ==

A contestant is on "Let's Make a Deal". She is told that behind one of
three curtains there is a new car. Behind the other two curtains are
dirty
old goats.

She picks a curtain. Before it is opened, one of the other curtains is
opened to reveal some dirty old goats.

She is then given the opportunity to change her mind about which
remaining
curtain she thinks the car is behind.

What should she do?

=============================================== =

Surprisingly, I chose what is considered to be the correct answer.
I'll let those that have never heard of this think about it and decide
for
themselves.

It's simple. There are two doors left which leaves three choices. Of
the three choices, two probabilities exist that she wins the car by
switching her choice.

She switches her choice to increase the probability of winning the
car.

Doesn't make sense.
She made her choice when the odds were 2:1 against her.
Since one curtain was eliminated, the odds are now 1:1.
Changing her choice won't change the odds.
The odds changed when the first curtain was opened.
Flip a coin 10 times and it comes up heads each time.
What are the odds of heads on the 11th flip?
Same as they were on the first flip. 1:1.
Or even money for you real gamblers.
Of which Galactic guys don't qualify.
Unless you're wagering quateros on warpsnerk lightbeam racing.

--Vic



Tom was correct, although I am not sure why.

Her probability of winning increases from 33.3% to 66.6% by changing her
initial pick. The majority of people do not get this right and don't
understand why.

This is a classic mathematical probability exercise that has been bashed
about for years by everyone from math PhD's to grammar school whiz kids.

When she first picked a curtain, she had a 2 in 3 chance of being wrong.
That didn't change after the first curtain with goats was opened. But it
does change if she changes her choice, and it can only increase her chances
of being correct.

Here's another explanation:

http://mathforum.org/dr.math/faq/faq.monty.hall.html

Eisboch

FWIW!! Whoops!
 

On Fri, 30 Jan 2009 04:22:27 -0500, "Eisboch"
wrote:



Tom was correct, although I am not sure why.

Only if the problem is expressed with the understanding that "Monty
knows."
IOW, if Monty knows, and *always* picks a door with goats behind it,
it changes the odds

Her probability of winning increases from 33.3% to 66.6% by changing her
initial pick. The majority of people do not get this right and don't
understand why.

This is a classic mathematical probability exercise that has been bashed
about for years by everyone from math PhD's to grammar school whiz kids.

When she first picked a curtain, she had a 2 in 3 chance of being wrong.
That didn't change after the first curtain with goats was opened. But it
does change if she changes her choice, and it can only increase her chances
of being correct.

That makes sense - but only when Monty always changes the randomness
with his knowledge. If Monty didn't know, 1/3 of the time he would
pick the car, making the contestant a loser
OTOH, if he didn't know, and picked the goats, it wouldn't do any good
for the contestant to change doors.
That's how I took the problem.
Good explanation by the guy below.
And it's well explained here
http://en.wikipedia.org/wiki/Monty_Hall_problem
Now, having proved I was right given how the problem was expressed and
my assumption of randomness, I'll admit I *might* have been fooled if
was expressed as "Monty knows." I'll never know now. But since it
wasn't, I'll just say I was right and leave it at that (-:

--Vic

http://www.tugbbs.com/forums/showthread.php?t=68845
(post #8)
"I'll try to explain it in words, without going through the math.
When you first select a door, there is a one-third chance that you
picked the correct door, and a two-thirds chance the correct door is
one of the two you did not pick.
Now, let's imagine a slight variation of the game. The rules are the
same, except that when Monty shows you a door he also has no idea what
is behind the door he picks. If Monty's door has the car, you lose and
the game is over. If Monty's door has a goat, you have the choice of
keeping your door or selecting another. Note that the only difference
between this and the "real" game is that Monty does not know what is
behind his door. Since Monty doesn't know where the car is, one-third
of the time he picks the car and you lose.
The other two-thirds of the time - when Monty's door has a goat - the
car is equally likely to be behind either door.. In that case it makes
no difference if you switch. Note that in this variation of the game
your odds of winning are one-third no matter what strategy you employ.
One third of the time you lose when Monty opens his door and you
aren't even given a chance to switch. Of the remaining two-thirds, you
win half of the time.
***
But Monty doesn't play the game that way. Monty knows what door has
the car, and when he picks a door he never picks a door that has a
car. IOW - Monty eliminates the one-third of outcomes where you lose
without having a chance to pick a door. (If you're a craps player,
it's like playing a craps game in which 2, 3 or 12 aren't craps - you
can never lose on the come out roll.)
Think about how that changes the game. Go back to when you first
picked a door. At that point there was a two-thirds chance that you
picked the wrong door. That situation remains. When Monty opens his
door, you now know that:
There is a two-thirds chance that the car is behind one of the doors
you didn't pick.
The car is not behind the door that Monty picked - which means that
there is a two-thirds chance the car is behind the door Monty did not
pick.
****
I think that what hangs up many people on the Monty Hall situation is
that they don't appreciate the significance of the fact that Monty
does not open a door randomly. In the first variant I laid out, Monty
does open a door randomly; in that case door switching doesn't make
any difference. But when Monty doesn't select a door at random, the
odds change.
__________________
Steve Nelson"

FWIW!! Whoops!
 

On Thu, 29 Jan 2009 22:53:28 -0600, Vic Smith
wrote:

Doesn't make sense.
She made her choice when the odds were 2:1 against her.
Since one curtain was eliminated, the odds are now 1:1.
Changing her choice won't change the odds.
The odds changed when the first curtain was opened.
Flip a coin 10 times and it comes up heads each time.
What are the odds of heads on the 11th flip?
Same as they were on the first flip. 1:1.
Or even money for you real gamblers.
Of which Galactic guys don't qualify.
Unless you're wagering quateros on warpsnerk lightbeam racing.

No. You thinking about it the wrong way 'round.

We're talking probabilities. Initially, she had a 1 in 3 chance when
she picked her first door. When Monty revealed the goats behind one
of the doors, her probability of choosing the correct door increased
to 2 in 3.

The key to understanding this is that the past can be ignored when
assessing the probability because it doesn't not matter which door the
player initially picks and which door the host opens. The second key
is that the host knows which door has the car.

It a variation of Bertrand's Box Paradox in which three boxes: a box
containing two gold coins, a box with two silver coins, and a box with
one of each are involved in a similar situation.

Draw out a decision tree - you'll see how it works.

--

If we aren't supposed to eat animals,
why are they made of meat?

FWIW!! Whoops!
 

On Fri, 30 Jan 2009 11:23:59 GMT, Wizard of Woodstock
wrote:


The key to understanding this is that the past can be ignored when
assessing the probability because it doesn't not matter which door the
player initially picks and which door the host opens. The second key
is that the host knows which door has the car.

And that he never picks the car. Answered this to Eisboch.
It's interesting. But only if you like thinking.

--Vic

FWIW!! Whoops!
 

Vic Smith wrote:

It's simple. There are two doors left which leaves three choices. Of
the three choices, two probabilities exist that she wins the car by
switching her choice.

She switches her choice to increase the probability of winning the
car.

Doesn't make sense.
She made her choice when the odds were 2:1 against her.
Since one curtain was eliminated, the odds are now 1:1.
Changing her choice won't change the odds.
The odds changed when the first curtain was opened.
Flip a coin 10 times and it comes up heads each time.
What are the odds of heads on the 11th flip?
Same as they were on the first flip. 1:1.
Or even money for you real gamblers.
Of which Galactic guys don't qualify.
Unless you're wagering quateros on warpsnerk lightbeam racing.

--Vic

You are correct if NO one knew which curtains hide the goats and which
one hide the car, but Monty Hall knows where the goat is hidden and
where the car is hidden and will open the curtain with the goat. When
you made your first guess, you have a 2/3 chance of losing, after he
opens the curtain with the goat, if you change your choice, you now have
a 2/3 chance of winning the car. If you make a diagram of the options
it will help you visualize the options.
--

Looking to for a good time?

click here to make yourself feel good.

http://tinyurl.com/d3vxvm

FWIW!! Whoops!
 

On Fri, 30 Jan 2009 05:31:46 -0600, Vic Smith
wrote:

On Fri, 30 Jan 2009 11:23:59 GMT, Wizard of Woodstock
wrote:


The key to understanding this is that the past can be ignored when
assessing the probability because it doesn't not matter which door the
player initially picks and which door the host opens. The second key
is that the host knows which door has the car.

And that he never picks the car. Answered this to Eisboch.
It's interesting. But only if you like thinking.

LOL!! 10-4.

--

"I have tried to know absolutely nothing about a great
many things, and I have succeeded fairly well."

Robert Benchley