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?