Thanks to Scottie's (http://www.stick-online.com/boards/index.php?topic=1979.0) topic it inspired me to make this one.
Quote from: Whitaker/vos Savant 1990Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
So what do you think it better to do. Switch or stay?
I don't really understand this problem. I've heard it before and remember that if you switch there is either a 1/2 or 1 chance of winning or something like that, but if you stay with the same door its always 2/3 chance of winning or something like that? I dunno I don't really get it, I feel like its a 50-50 shot either way, so you might as well stick with you're original choice, because the host might have only opened the door to purposely try to throw you off and make you switch your answer.
Why bother switching?
1/3 odds just turned to 1/2. So either way you have a 50% chance. Besides, always go with your first guess.
In a mathematical standpoint no because you have a 2/3 chance of winning now but in a logical stand point it really doesn't matter.
reayo is right. Its better to stick because you have a better chance than you do with switching. It does not turn 50/50.
From a psychological perspective the vast majority of society will switch their answer under pressure. Game shows take advantage of this, which is why you are always offered a second and sometimes third final answer. Knowing this, I personally would stick with my first answer.
raeyo is correct mathematically except the 2/3 is for switching not staying.
the chart for it is
original choice
stay switch switch
goat car car
if you stay you have a 1/3 chance of getting the car. If you switch you have a 1/3 chance for each of the 2 other options making it 2/3 chance of winning if you switch.
Not exactly because if you switch you create a 50/50 chance rather than a 2/3rd chance you acquire once one possibility was shown as a fraud. And 66.6666666 and so on is better than 50.
It's not vary intuitive. Great for a game show. :)
Well according to the internet sarithra is right. Oh well. But in reality it probably doesn't matter.
If anyone's ever read "The Curious Incident of the Dog in the Nightime" you'll know the answer. It goes into great detail explaining that, mathematically, switching is always the best choice, as you will have a better chance. Lol, saw this on the forums and remembered the book. :P
This one hurts my brain... I read the wikipedia article on it a bit, but it seems like they are intentionally using extremely complicated wording and convoluted thought processes.
I can accept that it's a false intuition to assume that each door is equal, but I can't comprehend how switching to the other door would give you a better chance...
Edit:
This page seems to help explain pretty well http://kasmana.people.cofc.edu/MATHFICT/montyhall.php?pg=explain
Basically, if you stay, you always have a 1/3 chance.
But, if you switch, the only time you lose is if you initially pick the car. If you pick either of the two doors that have a goat, then you always win because the other goat door is revealed. So you have a 2/3 chance.
Very interesting...
does it matter? A car or a goat would be a great prize!