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BGonline.org Forums
My favourite probability problem
Posted By: poseidon In Response To: My favourite probability problem (Stein Kulseth)
Date: Friday, 28 August 2009, at 1:10 p.m.
One, possibly wrong solution would be the following:
BEFORE Predictor's prediction you rationally decide that, due to the data, you do better choosing only the $1,000,000 envelope (if you choose both you will end up with $1,000). This way the predictor "scans and registers the state of every synapse in your brain" and predicts that you will choose only the $1,000,000 envelope and will reject the $1,000 envelope.
AFTER the prediction ,and due to the change on the data (you NOW know that the predictor has put the $1,000,000 in the first envelope) you RATIONALLY (not foxy) decide that you do better peeking both envelopes and ending up with $1,001,000.
Of course the aforementioned solution has two "pitfalls"
1) It rather impossible to follow that rational process without thinking in the first part (Before the prediction) THAT in the second part (after the prediction) you should change the decision. Only a computer could do that, or a human that by accident, does not think of it the first time, but does think of it AFTER the prediction. So if you do think that you should change your decision afterward, the Predictor will "scan and register the state of every synapse in your brain" and predict that you will peek both. As a result you will end up with $0!
2) The predictor probably can predict the future, no just read your thinking and conclude, so he will find what your final action will be. As a result you will end up with $0!
Given that the aforementioned solution is probably wrong the best solution is to choose the obvious: TAKE ONLY THE FIRST ENVELOPE WITH "ONLY" $1,000,000.
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