Argh my brain!
2008-Jun-28 |
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This afternoon I watched '21'. In it, the Professor of Maths played by Kevin Spacey described the Monty Hall problem, i'll try and explain it........
Imagine you're on a game show.
There are 3 doors.
Behind one of the doors, is a Car.
The other 2 doors are empty.
The host knows what door the car is behind.
You have to pick a door.
You pick door 1.
The host opens door 3. Nothing is in it.
He then says "do you want to stick with your door, or switch to door 2?"
If you stick with your door, you are almost twice as likely to lose as you are if you win.
This intrigued me.
To me, it would seem 50/50. Two doors left. Can only be one door. So, i'd stick to my door. Supersition on changing doors is too much.
So, how then, can I have a better chance of winning, if i pick the other door?
I'll try to explain the best I can, but bare with me, because I had to have this explained to me, given that it hurt my brain for the past four hours.
There is 100% chance that the car is behind one of those three doors. It's a certain.
Therefore, each door carries 33% of the odds.
-Door 1 - 33%
-Door 2 - 33%
-Door 3 - 33%
The door you pick, you only have 33% of getting it right.
Therefore, there is 66% chance of it being behind one of the other doors.
-Door 2 + Door 3 = 66%
Still with me? Prepare to be lost.
The Host is the key to the game. He KNOWS where the Car is. So, when he opens the door (lets say he opens Door 2), he knows it's not behind the door he's opening, which combined, are 66%.
Therefore, you now know that one of those with 66% odds is not the right door.
Logic tells you to switch to Door 3, because it's the one of the two with 66% odds that the Host didn't open, because he knew the car would be there. The host has effectively, helped you hugely.
If you stuck with your original choice, you'd only have 33% chance. Still a chance, but not great.
Therefore, you're 2/3 likely to win, if you switch than you are if you don't.
Confused?
Let me put it a little more simple. If there's 100 doors. And you pick one. Chances are, you've picked an empty one. So, if the Host goes and opens 98 of the those doors, leaving yours, and another one somewhere in the line, chances are, he's left the one with the car. So, you'd switch.
It's one of those puzzles, that makes me think, given that I hate Maths, and get's my brain working. Keeps me from being bored. I love things like this. If anyone else has one (except for 'the chicken or the egg'), then feel free to try my brain.
If you're ever on one of those kinds of game shows. SWITCH BOXES!
Wow, that hurt my brain just writing it out
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2008-Jun-28 - Untitled Comment |
| Posted by WelshPixie |
Maybe it's because I've been working with psychologists (stat whores) for the past five months, but that only took one attempt to be understood by my diminutive Neurone.
Wooh! |
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