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The two envelope problem
This one is fun to think about:
The two envelope problem is a famous paradox from probability theory (which we first presented on Plus back in September). Imagine you are given two envelopes, one of which contains twice as much money as the other. You're allowed to pick one envelope and keep the money inside. But just before you open your chosen envelope you are given the chance to change your mind. Should you stick with the envelope you picked first or switch? To find out write Since that’s bigger than |
The amount of money is not dependent upon what’s in your envelope. 2/3 of it is in one and 1/3 in the other. The expected value of the other envelope is 1/2*(1/3x+2/3x)=.5x, which is the same as the one you hold.
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Still haven't been able to get my mind around this thing :-(
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