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#### chisigma

##### Well-known member

Posted on 11 26 2011 on www.artofproblemsolving.com by the member mr10123 and not yet solved…

Daniel plays a game with a random number generator. It randomly selects an integer between 1 and n inclusive at the press of a button. If n is selected, he wins n dollars. If any other integer is selected, he loses 1 dollar. He keeps pressing the button until he has more than ‘even’ or he has more money than he begins with. Daniel’s disposable money is unlimited. What is the expected value of the number of times he must press the button?...Kind regards $\chi$ $\sigma$ |