A thief who is particularly knowledgeable about statistics and the legal system determines that if he commits a given heist the probability that he is never caught is 60%. If he is arrested he will go to trial where there is a 30% chance the jury will acquit him, a 30% chance he is convicted and serves a prison sentence less than five years, and a 40% chance the sentence is more than five years.
What is the probability that the thief is not imprisoned in 5 years?
What is the probability that the thief was arrested given that he is not imprisoned in 5 years?
