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Originally Posted by snarkophilus
This isn't true. The fact that you chose ball number 7 doesn't say anything about which urn is which.
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Answers like this always depend on the "rules". I'm reminded of the great Monte Hall puzzle, in which you are shown three doors, one of which is a grand prize and the other two are goats. After you choose one door, Monte reveals another door has a goat behind it. Then he asks you if you want to change your choice to the remaining door. Is there a reason to do it?
Depending on the "rules" governing what Monte does, the chance of the new door being the grand prize will either be 1/2 or 2/3. It's pointless to argue about which is correct until you know Monte's rules. (And given the way Monte normally works, the rules indicate the answer will be 2/3).