eli5: if a certain phenomenon occurs in 5% of a sample, does that mathematically mean it’s 5% likely to happen for any member of said sample? if yes, how?
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No. It means, if you pick a random member of the sample, there’s a 5% chance that it has the phenomenon.
This is subtly different than I think what you’re asking about, which is “Does every member of the sample have a 5% chance of the phenomenon?”…that would only be true if each individual member of the sample had the same distribution of the phenomenon and that’s not generally true.
For example, let’s suppose our phenomenon of interest is “cat” and we have a sample of 95 dogs and 5 cats. 5% of my sample is cats. If I randomly choose an animal from the sample there’s a 5% chance I choose a cat. But for each individual animal in the sample the distribution is 0/100…you either are a cat (100%) or you’re not (0%). You can’t have an animatl that’s 5% cat and 95% dog.
The same logic can be extended to continuous properties, like height. If I have a random mix of men and women and 25% of the sample is taller than 6′ that does *not* mean that each individual person in the sample has a 25% chance of being taller than 6′, because the height distributions for men and women are different.
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