Ok. Thanks for letting me know. I have removed the first example. I was thinking that it would make it simpler if I started out with an example that didn't look at evidence, but I think it is better without it.

If anyone wants to know the difference between frequency and probability. See the below quote:

“A probability is something that we assign, in order to represent a state of knowledge, or that we calculate from previously assigned probabilities according to the rules of probability theory. A frequency is a factual property of the real world that we measure or estimate. [...] The fundamental, inescapable distinction between probability and frequency lies in this relativity principle: probabilities change when we change our state of knowledge; frequencies do not. It follows that the probability p(E) that we assign to an event E can be equal to its frequency f (E) only for certain particular states of knowledge. Intuitively, one would expect this to be the case when the only information we have about E consists of its observed frequency.” Jaynes, E. (2003), Probability Theory: The Logic of Science, New York, Cambridge University Press, pg. 292