Goats and cars
There's a problem often used to show the unintuitive nature of probability, which has become very well known.
In that problem a contestant in a gameshow has to choose between three doors (A,B,C), on one there is a car, on the other two are goats.
After the contestant chooses, the host opens another door and shows a goat.
Then, the host offers the contestant the chance to switch his closed door for the other closed door.
Should he switch?
The intuitive answer is "it doesn't matter", because there's two doors and one car, so it's a 50-50 chance.
But the real answer is that it does matter, because it's a 33-67 chance!
While it's simple to show this to be the case to a statistically-educated dude, it's somewhat harder for a layman.
In fact, I think most explanations suck.
Here's my shot at it:
If you were offered the chance to switch between your closed door and the other two closed doors, would you take it?
The intuitive answer to that is of course, yes, because it's 67-33 for the car to be on the other two doors.
Now, regardless of where the car is, can the host open one of those two doors and show a goat? Of course, yes.
So, would you feel your odds went down because the host showed one of your two closed doors had a goat behind it? No, because he could always do that, and you know there was (at least) one goat there!
So, what difference does it make if one door is open or not?
I don't expect this to convince anyone, really, but just in case, I have a python implementation of this problem (goatcar.py :-) if anyone wants it, if empiricism can convince you ;-)
You missed out the important part - if you are in this situation, what should you do? Your options are:
1. stick with the original closed door that you selected
2. change your choice to the remaining (non-chosen, non-opened door).
Answer: you should pick option 2, and change your choice to the remaining door. I think I recall reading about this on another blog a while back, can't remember where.
(PS. how about a comment preview please?)
Erm... that's all I am writing about ;-)
Quoting myself: "Should he switch?"
Comment preview... I didn't see that. Maybe I need a comment preview ;-)
It's really up to the pycs guys. I will file a wishlist...
I've heard it referred to as the "Montey Hall Problem."
Dangit.. Monty Hall. Good luck in searching for another Python implementation for that one...seems the OTHER show owns that googleshare.
Maybe I am weak in the gameshow department, but what other show?
I found this explanation convincing at the time:
After your first pick, you're stuck w/ a goat in 2 out of 3 cases. That's a lot. But in those cases, a switch will win you the car.