Hilary Taylor, the director of athletics at Green Hill College, must decide whether to conduct random drug tests of student athletes. About 50% of NCAA schools have institutional drug testing programs in addition to the NCAA's drug testing program.(Charles Feinstein reports on how decision analysis was used at Santa Clara University to recommend against a mandatory drug testing program in "Deciding Whether to Test Students for Drug Use," Interfaces 20, no. 3 [1990]: 80-87.)Ms. Taylor expresses payoffs in terms of cost; that is, positive dollar amounts correspond to a monetary loss. The goal is to minimize the cost. For simplicity, she ignores the wage paid to the employee who monitors the collection of the test sample and the fee that Green Hill pays the lab that conducts the test. She also ignores the cost of a true negative, even though an athlete who is not a drug user may feel that his or her privacy has been invaded by the testing procedure.Ms. Taylor assigns a zero cost to the accurate identification of a drug user and to the accurate identification of a nonuser. She assigns a cost of $1,000 to falsely accusing a nonuser and a cost of $500 to not detecting a user.Ms. Taylor's incomplete decision tree looks like this:

For the tree to be useful as a decision-making tool, branch probabilities are required. You are a work-study student in Ms. Taylor's office, and since you are taking a statistics course, she asks you to compute the branch probabilities for the decision tree. You decide to confine your analysis to ephedrine use by football players at Green Hill. In a 2005 study of substance use by student athletes conducted by the NCAA, 4.2\% of football players reported using ephedrine. You make the assumption that the prevalence of ephedrine use by football players is no different from that found in the NCAA study. Based on information provided by the lab that worm the the the ephedrine is 95\% reliable in both directions: P(+D)=0.95, and P(N)=0.95. The probability that a randomly selected Green Hill football player has a positive drug test result for ephedrine is 0.9122/0.0878/0.0399/0.0479. Given that a randomly selected Green Hill football player tests positive, the probability that he is not an ephedrine user is .9977/0.45444/0.0479/0.54556 Enter the branch probabilities on the decision tree. Ms. Taylor's optimal decision is to testot test football players for ephedrine use. For the tree to be useful as a decision-making tool, branch probabilities are required. You are a work-study student in Ms. Taylor's office, and since you are taking a statistics course, she asks you to compute the branch probabilities for the decision tree. You decide to confine your analysis to ephedrine use by football players at Green Hill. In a 2005 study of substance use by student athletes conducted by the NCAA, 4.2\% of football players reported using ephedrine. You make the assumption that the prevalence of ephedrine use by football players is no different from that found in the NCAA study. Based on information provided by the lab that worm the the the ephedrine is 95\% reliable in both directions: P(+D)=0.95, and P(N)=0.95. The probability that a randomly selected Green Hill football player has a positive drug test result for ephedrine is 0.9122/0.0878/0.0399/0.0479. Given that a randomly selected Green Hill football player tests positive, the probability that he is not an ephedrine user is .9977/0.45444/0.0479/0.54556 Enter the branch probabilities on the decision tree. Ms. Taylor's optimal decision is to testot test football players for ephedrine use