There are four possibilities to consider. They are:
He is guilty and his blood matches.
He is guilty and his blood doesn't match.
He is not guilty and his blood matches.
He is not guilty and his blood doesn't match.
Here's the question I need help with:
Consider a hypothetical town with population 10,000 in which a man is suspected of a crime. His blood matches a stain found at the scene some time after the crime was committed. 1% of the population will have matching blood. Because in this case the stain is somewhat degraded, the probability of getting a match even if the blood is identical is 0.95
a) Draw a tree of the different possibilities of the man being guilty or not, and his blood matching or not.
b) Find the probability of a match.
c) Find the probability that this man is guilty of the crime and his blood matches.
d) If there is a match, find the probability that the man is guilty (use Bayes' rule)
Thanks in advance.