How are objective probabilites and statistics(frequency in the world) relevant to individual cases

I’m a bit confused about why objective probability(frequency in the world) should be relevant to individual cases?

Let’s say there is a frequency where 10% of the attending students successfully passes a specific test in mathematics and 90% fail.

Linda tells you that she has passed the test, but do not have any evidence except her own and a friends testimony that she attended and did pass. With the "claim" to have passed the test Linda is entitled to get 1 million USD from her grandfather.

The % that Linda is lying about passing the test is unknown.

How is the 10% pass rate among students relevant in assesing Lindas claim? How can we go from objective probabilities to Lindas case?

Are we entitled to believe Linda? How can we reason about this with statistics and probability?

Thanks for helping out