2. A class of 40 students goes on a school trip by bus. They stop at a historic site in a very isolated location, all get off the bus (including the busdriver), and the teacher explains the importance of the site to the class. One student (student A) excuses himself to go to the toilet, after which he rejoins the class. After the explanation the students, teacher and busdriver wonder around the site for 30 minutes. When they all return to the bus it is clear that the bus has been broken into. Student A is immediately the rst suspect, especially because a small sample of the cotton of a sweatshirt is found at the door that is broken into, and at rst sight this seems to be the same material of the sweatshirt that student A is wearing. A lab analysis afterwards conrms that there is a 0.95 probability that the cotton found at the door that is broken into is the same as the cotton of student A's sweatshirt. Given that it is impossible that anybody who was not travelling on the bus committed the crime, what is the probability that student A is guilty? ' Calculate the contingency table analytically, and. using this analytically obtained con- tingency table, the probability that student A is guilty