Here, something to fight over

F

FluerVanderloo

New Member
On another board I go to, someone posted this, and is arguing me tooth and nail. I want to know your responses before I tell you which side I took.

You are on a game show on television. On this game show the idea is to win a car as a prize. The game show host shows you three doors. He says that there is a car behind one of the doors and there are goats behind the other two doors. He asks you to pick a door. You pick a door but the door is not opened. Then the game show host opens one of the doors you didn't pick to show a goat (because he knows what is behind the doors). Then he says that you have one final chance to change your mind before the doors are opened and you get a car or a goat. So he asks you if you want to change your mind and pick the other unopened door instead. What are you're chances of getting a car if you decide to change your mind?
 
this is just like let's make a deal...i'd stick with what i have...old dude always tried to talk the people out of the winning door when they had it.
 
1/3....if you change your mind now there is only on option...the second of three doors
 
It'll always be one in three, there are three doors, you get to choose one. Whether or not you change your mind, you're still picking one of the three. The odds of winning don't change.
 
your inital gues was 1/3 chance. you now know that it is not one of the doors as that has been opened so you now have a 1/2 chance of getting it right.

1/3 = 2/6
1/2 = 3/6

Therefore you have a 5/6 chance of getting the right door.

OR

Lets call the doors a, b and c and then for a car we use p (prize) and for a goat we use g and the open door we use x

so
to start with we have
a b c
g p g

we have here a 1/3 chance of being right

we select door c

therefore we now have
a b c
x p g

so we have a 1/2 chance of being right

BUT

Here is the solution
[font=Verdana, Arial, Helvetica, sans-serif]You are on a game show on television. On this game show the idea is to win a car as a prize. The game show host shows you three doors. He says that there is a car behind one of the doors and there are goats behind the other two doors. He asks you to pick a door. You pick a door but the door is not opened. Then the game show host opens one of the doors you didn't pick to show a goat (because he knows what is behind the doors). Then he says that you have one final chance to change your mind before the doors are opened and you get a car or a goat. So he asks you if you want to change your mind and pick the other unopened door instead. What should you do?[/font]
[font=Verdana, Arial, Helvetica, sans-serif]Marilyn vos Savant said that you should always change and pick the final door because the chances are 2 in 3 that there will be a car behind that door. But if you use your intuition you think that chance is 50-50 because you think there is an equal chance that the car is behind any door.

Lots of people wrote to the magazine to say that Marilyn vos Savant was wrong, even when she explained very carefully why she was right. Of the letters she got about the problem, 92% said that she was wrong and lots of these were from mathematicians and scientists. Here are some of the things that they said I'm very concerned with the general public's lack of mathematical skills. Please help by confessing your error.

[/font][font=Verdana, Arial, Helvetica, sans-serif]Robert Sachs, Ph.D., George Mason University,
[/font][font=Verdana, Arial, Helvetica, sans-serif]There is enough mathematical illiteracy in this country, and we don't need the world's highest IQ propagating more. Shame![/font]
[font=Verdana, Arial, Helvetica, sans-serif]Scott Smith, Ph.D., University of Florida'
[/font][font=Verdana, Arial, Helvetica, sans-serif]I am in shock that after being corrected by at least three mathematicians, you still do not see your mistake.[/font]
[font=Verdana, Arial, Helvetica, sans-serif]Kent Ford, Dickinson State University,
[/font][font=Verdana, Arial, Helvetica, sans-serif]I am sure you will receive many letters from high school and college students. Perhaps you should keep a few addresses for help with future columns.[/font]
[font=Verdana, Arial, Helvetica, sans-serif]W. Robert Smith, Ph.D., Georgia State University,
[/font][font=Verdana, Arial, Helvetica, sans-serif]You are utterly incorrect . . . How many irate mathematicians are needed to get you to change your mind?[/font]
[font=Verdana, Arial, Helvetica, sans-serif]E. Ray Bobo, Ph.D., Georgetown University,
[/font][font=Verdana, Arial, Helvetica, sans-serif]If all those Ph.D.'s were wrong, the country would be in very serious trouble.
Everett Harman, Ph.D., U.S. Army Research Institute. But Marilyn vos Savant was right. And here are 2 ways you can show this:[/font]
CuriousChart.jpg
[font=Verdana, Arial, Helvetica, sans-serif]
So if you change, 2 times out of 3 you get a car. And if you stick, you only get a car 1 time out of 3.
[/font]
[font=Verdana, Arial, Helvetica, sans-serif]And this shows that intuition can sometimes get things wrong. And intuition is what people use in life to make decisions. But logic can help you work out the right answer.[/font]
[font=Verdana, Arial, Helvetica, sans-serif]It also shows that Mr. Jeavons was wrong and numbers are sometimes very complicated and not very straightforward at all. And that is why I like The Monty Hall Problem.[/font]
Click to expand...


taken from http://www.randomhouse.ca/readmag/volume4issue1/excerpts/curious.htm
 
How many miles per gallon can yer get from the average goat? (I already have a car) :)
 
Oz said:
How many miles per gallon can yer get from the average goat? (I already have a car) :)
Click to expand...
i dunno about gas mileage but they can be used for lawn...er..maintenance. ;)
 
The way you describe it, your first guess is irrelevant, as the second guess is the ultimate decision and will always be 50/50 no matter which of the 3 doors you chose first. If you choose a door with a goat, they'll eliminate the other goat door and leave you two choices: stay or change, in which case your odds are 50/50. If you choose the door with the car, they'll eliminate one of the goats leaving you again two choices: stay or change, and your odds are once again 50/50. It's just a little mind game, see whether people will stick with their choices or change their minds when they think their odds have improved when in fact they haven't changed one bit.
 
After reading all of that, it seems to me that it is all a matter of how you look at it. Whether you think with probability or logic is your choice, hence two different answers. It's not fair to choose only one right asnwer, as both are technically correct.
 
peterska2 said:
your inital gues was 1/3 chance. you now know that it is not one of the doors as that has been opened so you now have a 1/2 chance of getting it right.

1/3 = 2/6
1/2 = 3/6

Therefore you have a 5/6 chance of getting the right door.

OR

Lets call the doors a, b and c and then for a car we use p (prize) and for a goat we use g and the open door we use x

so
to start with we have
a b c
g p g

we have here a 1/3 chance of being right

we select door c

therefore we now have
a b c
x p g

so we have a 1/2 chance of being right

BUT

Here is the solution
[/size][/font]

taken from http://www.randomhouse.ca/readmag/volume4issue1/excerpts/curious.htm
Click to expand...


This is EXACTELY why I failed the math part of the GED Test-URGHHHHHHHHHHH.................................
 
FluerVanderloo said:
After reading all of that, it seems to me that it is all a matter of how you look at it. Whether you think with probability or logic is your choice, hence two different answers. It's not fair to choose only one right asnwer, as both are technically correct.
Click to expand...

So which one did you go for?
 
Stop Laughing said:
The way you describe it, your first guess is irrelevant, as the second guess is the ultimate decision and will always be 50/50 no matter which of the 3 doors you chose first. If you choose a door with a goat, they'll eliminate the other goat door and leave you two choices: stay or change, in which case your odds are 50/50. If you choose the door with the car, they'll eliminate one of the goats leaving you again two choices: stay or change, and your odds are once again 50/50. It's just a little mind game, see whether people will stick with their choices or change their minds when they think their odds have improved when in fact they haven't changed one bit.
Click to expand...

Dead on. Once you eliminate one door and get the option to change (i.e. reset your chances), the odds become 50/50 whether you change or not.
 
HomeLAN said:
Dead on. Once you eliminate one door and get the option to change (i.e. reset your chances), the odds become 50/50 whether you change or not.
Click to expand...

Yep, I missed the part about opening the one door. Gotta work on that old reading comprehension. :lol:
 
I concur with the 50/50. Since you ALWAYS eliminate a door with no prize, you should remove it from the equation since it is always true.

Look at the pic that ska posted and eliminate a door with a goat, then see how the probabilities of getting a car or a goat are equal.

50/50
 
50/50 you are now choosing between 2 doors, the door you eliminated is out of the equation, now you have chosen one door, and he offered you the choice of the other one, so you have 2 choices, stay with your door, or choose the other.

2 choices = 50/50
 
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