Let’s say that I am evaluating the probability that a person is guilty of murder. The person who the police have decided to prosecute is tall, was a friend of the victim, was out drinking the night of the crime, lived in or was in town the day of the murder, and suffered a sprained shoulder the night of the murder.
Further, I am told that these are the probabilities of guilt for each of these pieces of evidence:
3 in 4 times, the murderer will be someone who was drunk.
2 in 5 times, the murderer will be someone who was a friend (but not lover).
9 in 10 times, the murderer will be someone tall (not 10 in 10, because the CSI person may have misjudged something).
1 in 5 times, a wound like a sprained shoulder would occur during a murder as opposed to random chance / drunkenness / etc.
How do I compute my confidence rating that the tall friend was guilty? I.e., like 95% certainty, given a population size of about 100,000 people who would have been in town at the time, and a friend pool of about 30.
Not a homework problem.