There is a set of 100 randomly generated integers and we know that 50 are odd and 50 are even. If we divide this set into two subsets of random sizes, choosing the contents based on characteristics unrelated to eveness, what is the probability that within each such subset the distribution of odd-even integers is equal (=p), e.g. 20-20 in one and 30-30 in the other?
Is it possible to calculate p without knowing the specific sizes of both subsets?
When analyzing subsets after knowing their size I thought the proper way is to use the binomial distribution formula for one subset having equal distribution as the second one will then have to follow this pattern given that the total number of even and odd integers is equal. However, this seemingly causes two different p's for the same event as the probability of equal distribution will be always higher in the smaller subset,even though its content is not independent of the larger subset.
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