1. ## probability calculation question

I have a room and in this room are a lot building blocks. I have 100 rows and each row contains 60 building blocks with 20 red, 20 blue and 20 green building blocks. About the right 50 building block rows I know that they are randomly arranged. About the left 50 building block rows I suppose that they are arranged not randomly, but I don't know it for sure. So I try to find a pattern that describes the 50 left rows to compare it with the 50 right rows. I create a pattern like: "Viewing one building block after another there will be a green block. Until the next red block there will be no blue block. Until the next green block there has to be exactly 2 blue blocks...". I find out that this pattern matches for all 50 left building block rows. I test it now on the right 50 rows and find out that the probability that this does fit is about 0.1 (5 rows fit, 45 don't fit).

Is it now true that the probability that this pattern is created by chance is p = 0.1^50 = 10^(-50) ?

2. ## Re: probability calculation question

Yes - based on an estimate that probability of the pattern occuring is 0.1, the probability of it happening 50 times in a row is (0.1)^50. To be honest I don't understand your description of the pattern, but as long as it's well defined this probability calculation should be good. However, this assumes the pattern you describe is not based on what you see in the left rows - i.e. the pattern is something pre-defined.