You are told there are two envelopes. One contains twice as much money as the other one. You pick one but are allowed to change your mind after picking it. (You are equally likely to pick the one with less money as the one with more money.)
To figure out how much on average the other envelope should contain, one might average x/2 and 2x because one is equally likely to pick one as picking the other. Since this comes out to 5x/4, one might always change his or her mind. But wouldn't this end up with one never making up his or her mind?
It wouldn't matter, as long as you didn't know anything about either envelope.
Say you picked one (50% chance it is the 2x one) and then you switch, it's is still 50% it will be 2x one.
But, another thought is that it wouldn't matter because if you picked one and opened it, you would see the money and not know whether it was the 2x or the x (assuming the person doesn't say). i.e. If you open it and see 10000$ you won't know if the other envelope contains 5000$ or 20000$...
Posted by patel
on 2005-03-14 05:53:06