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Unformatted text preview: i th name with probability 1 i . At the end, choose whichever name you were remembering. Prove that with this process, all the names on the list are equally likely to be chosen. 5. A bunch of people each pick a number from 1 to n . Then they take the sum of all the numbers mod n . Prove that all outcomes are equally likely if one person picks a number uniformly at random (so all are equally likely) and independent of the other players choices. 6. Prove that there is no way to load two dice so each possible sum , from 2 to 12, is equally likely. (By load the dice, we mean set up the probabilities for each number on each die. The dice remain independent.)...
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This note was uploaded on 03/14/2012 for the course MATH 55 taught by Professor Strain during the Summer '08 term at Berkeley.
- Summer '08