I am still a bit confused about the setup of the problem. 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? If so, shouldn't

be relevant? If a single point is all we have, call it the binary variable

- equal to 1 if the patient has a heart attach; 0 if he doesn't-, that would be the probability of generating a single point with a patient having a heart attack, given the underlying probability that a person has a heart attack, right? In that case, the posterior is going to have two cases

and

. The question refers only to case

right?