Chance of something happening.

  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. 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. That makes sense. And yeah, I meant "at least", but "exactly" would be a good one to know, too. Thanks.
  5. 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. 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. 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. Ahh I gotcha. Thanks. :)
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