Author: Paolo Casaschi
Date: 07:21:07 01/09/02
Go up one level in this thread
I had the same problem and I found that an EXCELLENT way to convince people is to extrapolate. So you tell your friend: let's doit now with 10 doors. You pick one. Then I'll open 8 out of the remaining 9 and you are offered to switch. What would you do ? Then you doit with 1000 doors, yuo pick one and I'll open 998 out f the remaining 999. Then you doit with 1 million doors. You pick one. Now, out of 1 million it is very likely that you did not pick the right one, so if I open 999998 out of 999999 remaining what would you do ??? It is easy to show that, with N doors, the first pick of your friend divided the set of doors in two groups, the selected door (with probability 1/N of being the right one) and the other (with probability (N-1)/N that one of these is the right one). The fact that I open N-2 doors DOES NOT ADD ANY ADDITIONAL INFORMATION about the probability of the two sets above, because in any case I will be able to open N-2 doors without the price behind. Usually the one million example works. If it does not, play the game with one million doors, one buck a shot and they will convince quickly (or you get rich). --Paolo
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