Answer

I am not familiar with any statistical logic here. It seems to me that this is more of a legal determination than a statistical one. And even on the legal plane, this rule has taken on dimensions that are hard to understand. There are cases in which one can perhaps make sense of it, but its applications go far beyond those.
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Questioner:
Could it be that the Sages derived this rule from an incorrect statistical understanding? (Maybe like Pascal, who thought the probability of God’s existence was 50%.)
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Rabbi:
Possibly, though when it comes to the applications I have my doubts. Anyone understands that statistically there is no difference.
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Questioner:
What difficulty did the Sages have with using the rule "Whatever separated is presumed to have separated from the majority" even in situations of something "fixed"?
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Rabbi:
I don’t know. I am not familiar with a logical explanation for the fixed-case rule (search online; there is an article by Uman on this, but if I remember correctly I did not agree with it, at least not in all cases).