# How are objective probabilites and statistics (frequency in the world) of groups related to individual cases?

I'm a bit confused about why frequentist measures of probability based on groups are relevant to individual cases. It seems that moving from the group to the individual is somehow a violation of the fallacy of composition or is a hasty generalization.

Let's say there is a frequency where 10% of the attending students successfully pass a specific test in mathematics and 90% fail. Linda tells you that she has passed the test, but you do not have any evidence except her own and a friend's testimony that she attended and did pass. If Linda has passed, she is entitled to get 1 million USD from her grandfather. And no presumption can be made about the likelihood of Linda lying about passing.

How logically is the proposition of the 10% pass rate among students related to the assessment of Linda's individual testimonial claim? Perhaps more precisely what is the logic or argument that can be applied regarding frequentist probabilities?

• David Lewis's principal principle might be of interest to you. "The Principal Principle says that a rational agent conforms their credences to the chances." Of course here we have additional information, namely whatever we know about Linda in particular, and how reliable Linda's testimony is, so we conditionalize on those piece of information too. If Linda's a good student, and she rarely lies then it should be very likely that she passed. Dec 5, 2020 at 11:35
• Many Thanks Adam! I've started to study probability of causation as well. Dec 7, 2020 at 19:57
• Hi, welcome to Phil.SE! Can you cite, or provide more information, on the theory you present as popular? Sure we learn from probability to singular cases, but this is a bit extreme with many parameters which you claim to not be considered in the statistics. And if the question ends up being simply about theory of probability, it probably doesn't belong in this SE but rather on Math or Statistics. Dec 29, 2020 at 20:53
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– J D
Jan 3, 2021 at 15:52
• Edited in response to multiple closure votes.
– J D
Jan 3, 2021 at 16:23