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Math Help - Determining that an event is not random with a given confidence

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    Determining that an event is not random with a given confidence

    Lets say I have a bag with three marbles in it, one red and two blue. I ask people to try their best to pick the red marble. I'd like to determine how many succeses it will take to be able to say "with 95% confidence Mike can't tell the difference". For example, maybe the red marble has a slightly rougher finish on it, which will allow someone to choose it once they figure it out. If they make 0 out of 20, the chances of that happening randomly is .0003, pretty likely they can't tell the difference.

    I constructed a modified pascal triangle to get the likelihood of drawing x successes out of n draws:
    Code:
          x
         0     1     2   3    4 
    n
    1    2    1   
    2    4    4     1   
    3    8    12   6    1   
    4    16   32   24   8   1
    The sum of each row is 3^n, so the probability of each scenario is the pascal number divided by 3^n. I was thinking that I could say the person is not successful when the pascal number/3^n is less than .05. However, if I choose lower confidence intervals, there's a point around .8 where EVERY value is less than the confidence interval

    Because of this I thought maybe the best way is to look at what the probablility is of getting x or fewer out of n. This gives me values, but I don;t know if this is the right way of looking at the scenerio.

    Kevin
    Last edited by Beakerboy; January 14th 2010 at 01:19 PM. Reason: formatting
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