I'm having problem wrapping my head around the following scenario:
Suppose there's a gory murder in the island of Onewaynia. Two persons have been shortlisted (and it's guaranteed by divine forces that one and only one of them is the murderer), Mr X and Mr Y. The common people don't know who are shortlisted however (they don't know the identity of X/Y), however the commissioner do.
Morever, suppose that there's traces of blood AB near the murder scene and it's guranteed the murderer has blood AB. Among the general population, 1 % (i.e with probability 0.01) people has blood AB.
Person X is tested to have blood AB. The blood group of Y is not tested. What's the probability that Y has blood group AB, if you (a) Ask the commissioner (b) Ask a common man ?
I am having very confusions with this problem. Isn't the probability of Y having blood group AB is 0.01 regardless of who you ask ?
But the book is telling that the commissioner would tell that Y has a higher chance of having blood group AB because Y has 50% chance of being the murderer. But can't the commissioner just ignore the information that Y is shortlisted the murderer and churn of the answer of p = 0.01 ?
Why should the truth value depend on the person you're asking ? Why having the knowledge that Y is shortlisted (but not knowing any other thing about Y) increases the probability ?