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.