Quote:
Originally Posted by fgpancorbo
Is it correct to assume that what we are trying to determine is the underlying probability of somebody picked at random from the population to have a heart attack out of a single sample?

(emphasis added)
It should be
based on rater than
out of. A source of confusion here is that
is a probability, but then we have a probability distribution over
. Let us just call
the fraction of heart attacks in the population. Then the problem is addressing the probability distribution of that fraction  Is the fraction more likely to be 0.1 or 0.5 or 0.9 etc. The prior is that that fraction is equally likely to be anything (uniform probability). The problem then asks how this probability is modified if we get a sample of a single patient and they happen to have a heart attack.
If I have not answered your question, please ask again perhaps in those terms.