In a study of drug testing of Olympic athletes at the university of Texas in 2004 an athlete was either and illegal user or not an illegal drug user. Let U denote an athlete who is an illegal grug user and let NU denote an thlete who is not an illegal drug user. Assume relative frequencies give P(U)=0.15 and and P(NU)=0.85. A drug test is available to test weather an athlete is a user or not. It may be positive, denoting a user, or negative, denoting a non user. Let a positive drug test be denotes as T+, adn a negative test be denoted as T-. Suppose it is known that P(T+IU)=0.06 and P(T+INU)+0.12.
(a) If an athlete tests positive what is the probability the athlete is a user?
(b) If and athlete tests negative, what is the probability the athlete is not and illegal user?
(c) What is the probability of a false positive?
(d) If an athlete tests negative what is the probability the athlete is a user? (i.e. P(false negative))