A lie detector will show a positive reading 10% of the time when a person is really telling the truth, and a lie detector will show a positive reading 90% of the time when a person is in fact lying. The lie detector is tested on three subjects. The first subject is (secretly) known to lie to every single question, no matter what the question (Remind you of anyone?). The second lies to 70% of all questions, and the third lies to 10% of all questions. a. What is the probability that the lie detector shows a positive on all three subjects?b. What is the probability that the lie detector shows a negative on all three subjects?c. What is the probability the lie detector shows a positive on the first subject and a negative on the other two subjects?d. Given that the lie detector showed a positive result on exactly one subject, what is the probability that subject was the first one?e. Given that the lie detector showed a positive result on exactly two subjects, what is the probability those two subjects were subjects 1 and 2?f. Given that the third subject told the truth, what is the probability the lie detector incorrectly concludes he lied? This is called a false positive reading.