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Chance of something happening.

  1. May 26, 2008 #1
    This has bugged me for quite some time now, but I've always shrugged it off. I've taken a course in statistics and have dealt with them in one way or another for a few years, so I KNOW I've seen the answer to this, but I can't remember it and don't know where to look for it.

    Well, I could crack open my statistics book, but I figure this would go faster.

    Anyway, my question is as follows: The probability of something happening is 1/100. You do 100 iterations. What is the chance of it happening?

    So for example you have a 100 sided die, and you roll it 100 times. What's the chance of getting a 9? I know I can't be 1. But it has to get closer as you get to infinity, right? I just can't think off the top of my head how that formulation would go.
  2. jcsd
  3. May 26, 2008 #2
    What is the chance of getting exactly one nine or at least one nine?

    I think at least one nine is 1-.99^100
  4. May 26, 2008 #3
    That makes sense. And yeah, I meant "at least", but "exactly" would be a good one to know, too. Thanks.
  5. May 26, 2008 #4
    I had to double check this one:

    Exactly one nine is C(100,1)(.01^1)(.99^99)
    then exactly two nines C(100,2)(.01^2)(.99^98)
    and so on...
  6. May 27, 2008 #5
    Oh, duh, it's a combination.

    Okay, but do you have a quick derivation for getting at least 1 number? It's not obvious to me how you would get that from seeing the formula, but I suspect it has something to do with combinations anyway.
  7. May 27, 2008 #6
    I didn't derive it. I just considered not no nines. So the probability of any result of 100 rolls (1) minus the probability of all the rolls being any number but nine (99^100). In this case nine, but it doesn't matter. The probability is the same for at least one of any single number 1-100.

    I suppose you could sum the series of combinations. But that would be work I think.
  8. May 27, 2008 #7
    Ahh I gotcha. Thanks. :)
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