This is a well known problem that illustrates a nice area of proability/statistics (recently showed up inthe so so movie with Kevin Spacey, 21):
In a game show, a contestent has to guess which of three doors
the prize lies behind (e.g. a fast car) - the other two doors lead to nothing.
The game show host knows the right answer.
Now, lets say the contentst guesses door A. The game show host
now opens one of the other two doors (obviously showing
nothing), and asks the contestent
if they want to stay with their choice, or change to the door that
they didn't chose and the host didn't open.
What should the contestent do, and why?
So the answer is change (always - since you have 2/3 chance of the prize being behind the two doors you didn't pick, and in the second go, you get to know it is 50/50 between the door you did pick (with 1/3 chance) and the one you didnt that didnt get opened, so either way, you are twice as likely to win by changing as by sticking.
The more interesting problem is:
how do you convey this (teach it) to people?
I asked 4 random kids - 2 got it (using the 1/3 v. 2/3 or the 50/50 v 1/3 argument above) . two refused to believe me after explanation
Soome said: cast the change in information as like recharging in a game, then maybe they'd get it - so information increase is entropy decrease entropy is just negative heat. maybe there is something in this - could we devise a game whch illustrates this idea generally?
derek says: why not do the 100 (or million) door version and in 2nd go, host opens 999,998 doors...