An athletic league does drug testing of its athletes, 10 percent of who use drugs. This test, however, is only 95% reliable. That is, a drug user will test positive with probability .95 and negative with probability .05, and a nonuser will test negative with probability 0.95 and positive with probability .05.
Develop a probability tree diagram to determine the posterior probability of each of the following outcomes of testing an athlete.
(a) The athlete is a drug user, given that the test is positive.
(b) The athlete is not a drug user, given that the test is positive
(c) The athlete is a drug user, given that the test is negative.
(d) The athlete is not a drug user, given that the test is negative.
(e) IMPORTANT: Use the Excel template for posterior probabilities to check your answers in the preceding parts.
An athletic league does drug testing of its athletes, 10 percent of who use drugs. This...
An athletic league does drug testing of its athletes, 10 percent of who use drugs. This test, however, is only 95% reliable. That is, a drug user will test positive with probability .95 and negative with probability .05, and a nonuser will test negative with probability 0.95 and positive with probability .05. Develop a probability tree diagram to determine the posterior probability of each of the following outcomes of testing an athlete. (a) The athlete is a drug user, given...
The college suspects their star player James Strongarm has used an illegal performance-enhancing drug. Currently, the probability that James is a drug user is 0.37. They consider barring him from athletics. The real "monetary" values of the outcomes are difficult to assess in this case and, therefore, the value of each outcome is expressed in a funny money unit: Galleon (from Harry Potter Movies). The following are the payoffs for the potential outcomes: Correctly identifying a drug user and barring...
The college suspects their star player James Strongarm has used an illegal performance-enhancing drug. Currently, the probability that James is a drug user is 0.37. They consider barring him from athletics. The real "monetary" values of the outcomes are difficult to assess in this case and, therefore, the value of each outcome is expressed in a funny money unit: Galleon (from Harry Potter Movies). The following are the payoffs for the potential outcomes: Correctly identifying a drug user and barring...
Assume that Limitless Labs, Inc., offers three basic drug-testing services for professional athletes. Here are its prices and costs: Price per Unit Variable Cost per Unit Units Sold per Year Basic $ 500 $ 120 850 Retest 800 400 100 Vital 4,000 2,800 50 Variable costs include the labor costs of the medical technicians at the lab. Fixed costs of $390,000 per year include building and equipment costs and the costs of administration. A basic "unit" is a routine drug...
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