I have question about the urn model. Suppose I have an urn:
Model A: Either the urn has 100 balls in it of which 70 are black and 30 are white. Model B: Or the urn has 100 balls in it which are indeterminate in color. When removed, they turn black with probability 0.7 and white with probability 0.3.
I am only allowed to sample balls from the urn one at a time, and must replace each ball after noting its color.
Is there any statistical test I can perform that would help me determine which type of urn it is?
Is it also true that I could replace the models by:
Model C: The urn has 1 ball in it which is indeterminate in color. When removed, it turns black with probability 0.7 and white with probability 0.3. Model D: The urn has 10 balls in it of which 7 are black and 3 are white.
Does this mean that there are an infinite number of different models which would be indistinguishable by statistical sampling?