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Probability problem driving me crazy!

  1. Jun 18, 2010 #1
    So I'm going to the casino this weekend and it got me thinking about probability.

    If I have an n-sided die and roll it n times, what are the chances of me hitting a specific number, x?

    For example, if I flip a coin (n=2) twice, what are the chances of me hitting heads at least once?

    Answer (obvious for n=2): 1-.5^2 = .75

    It's obvious for most n's until they get large. I've simplified it to this equation:

    1-((n-1)^n)/(n^n)

    If I go back to n=2, we see that we arrive at the same answer of .75.

    My TI-89 can calculate up to an n of 100, which gives a value of .6340.

    I'm very interested in this value as n increases, though. Unfortunately I don't have access to math software that could solve the problem as a limit. How can I solve this, or more importantly... WHAT'S THE ANSWER?

    It's driving me crazy! My best guess is that it tends towards 1/2.

    Thanks for any help!
     
  2. jcsd
  3. Jun 18, 2010 #2
  4. Jun 19, 2010 #3

    uart

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    Science Advisor

    Yes the [itex]\left(\frac{n-1}{n}\right)^n[/itex] term aproaches [itex]1/e[/itex] so the limiting probability DyslexicHobo seeks is [itex]1 - 1/e[/itex], which is about 0.632
     
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