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

1. ## 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