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pmsumner at 02:05am on 07/02/2002
pmsumner at 02:05am on 07/02/2002This is a fantastic page which demonstrates the Monty Hall Problem (3 doors, 2 goats, one prize car).
The basic problem: You're on a game show, and are shown three doors. Behind one door, is a car. Behind the other 2 doors, are goats. You pick a door. No matter what door you pick, the host then shows you what's behind another door - and surprisingly not, the door always always ALWAYS conceals a goat.
He then gives you the option of switching the door you chose. Should you switch the door - or should you stick to your original choice?
This is an intriguing question - one that had me confused for ages when I first heard it, but then I saw the light :)
The basic problem: You're on a game show, and are shown three doors. Behind one door, is a car. Behind the other 2 doors, are goats. You pick a door. No matter what door you pick, the host then shows you what's behind another door - and surprisingly not, the door always always ALWAYS conceals a goat.
He then gives you the option of switching the door you chose. Should you switch the door - or should you stick to your original choice?
This is an intriguing question - one that had me confused for ages when I first heard it, but then I saw the light :)
(no subject)
But I've spent a *long* time trying to explain it to some other people!
(no subject)
(no subject)
So in that case you know *precisely* what I mean.
You wouldn't believe how many members of a Mensa mailing list refused to believe me, though...
(no subject)
I guess I'm going to have to sit down and mull this over a bit. Maybe ask my friend Jeana to explain it - she's got her Master's Degree in Sadistics - err, Statistics. :)
Truth be told though, as for myself, I'd prefer winning the goat over the car anyway...
(no subject)
Keep at it, it makes sense in the end...
(no subject)
I've also sat down - thought it over - and yes, it does make a lot of sense... Here's my take on it:
You pick one of 3 doors... the odds that the 'car' is behind the door you pick is 1/3... the odds its behind one of the other doors then is 2/3. So it's twice as likely one of the 2 doors you didn't pick has the car behind it...
You also know for certain that at least one of the doors you did not pick has a goat behind it - so when the host opens a door you didn't pick and shows you a goat there is no new information here - and showing you this doesn't change the odds any, its still twice as likely that the car is behind one of the 2 doors you didn't pick!
So if its still twice as likely that one of the 2 doors you didn't pick has the car behind it - and you know which one of those doors has the goat behind it... then it only makes sense to switch!
I, however, would still prefer winning the goat over the car.
But of the 2 doors you didn't pi