Since 0000 is considered a possibility there are a total of 10000 sequences possible since numbers can repeat. That means there is a 1 in 10000 chance of winning. The expectation of this game is the probability of winning multiplied by the reward minus the probability of losing multiplied by the loss. So if you win the game you will make a return of 4999 (because you paid a dollar). The loss would be a dollar. So 4999 x 1/10000 - 1 x 9999/10000 = -0.5. So the expected value is -$0.50. Hope this helps. Let me know if you have any questions

May 16th, 2015

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