The college suspects their star player James Strongarm has used an illegal performance-enhancing drug. Currently, the...

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The college suspects their star player James Strongarm has usedan illegal performance-enhancing drug. Currently, the probabilitythat James is a drug user is 0.37. They consider barring him fromathletics. The real "monetary" values of the outcomes are difficultto assess in this case and, therefore, the value of each outcome isexpressed in a funny money unit: Galleon (from Harry PotterMovies). The following are the payoffs for the potentialoutcomes:
Correctly identifying a drug user and barring this person fromathletics: 40 Galleon
Falsely accusing a nonuser and barring this person fromathletics: -60 Galleon
Not identifying a drug user and allowing this person toparticipate in athletics: -30 Galleon
Not barring a nonuser: 0 Galleon
Before they make the decision, they can ask for a drug test,which costs -1 Galleon per single athlete . In the drug testing,assume there are two possible test results: positive and negative.For a drug user, the probabilities of these outcomes are 0.95 and0.05, respectively. For a nonuser, they are 0.01 and 0.99,respectively. Assume that 2% of all college athletes are drugusers.
(When you use the probabilities from the flipped table, use cellreferences in the decision tree instead of typing the probabilitiesmanually. All choices in the following questions are based on thedecision tree built using this practice.)
Question 5 (1 point)
What is the EMV of making the decision without the test?
A -58.6
B -24
C -12.1
D -11.1
Question 6 (1 point)
If the first decision is to do the test or not and the seconddecision is to bar or not, what is the EMV of the whole tree? (Dueto the rounding error, your answer may not match perfectly with thecorrect choice. Pick the choice closest to your answer.)
A -0.858
B -0.269
C 0.142
D 2.678
Question 7 (1 point)
What is the best decision alternative?
A Forgo the test and bar him.
B Forgo the test and do not bar him.
C Take the test. Bar him if the result is positive; do not barhim if the result is negative.
D Take the test, and do not bar him.
Question 8 (1 point)
If the test costs -10 Galleon, what is the best decisionalternative?
A Forgo the test and bar him.
B Forgo the test and do not bar him.
C Take the test. Bar him if the result is positive; do not barhim if the result is negative.
D Take the test, and do not bar him.

Answer & Explanation Solved by verified expert

4.3 Ratings (831 Votes)

SOLUTIONCalculate conditional probabilitiesDecision tree is as followsEV of node B 37406360 23EV of node C 3730630 111EV of node G 659740340360 5972EV of node H 65973034030 19792EV of node J 001040999060 59897EV of node K 00103099900 00309EV of node D 0288MAX5972 19792 9712MAX598970309 0142EV of node See Answer

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The college suspects their star player James Strongarm has usedan illegal performance-enhancing drug. Currently, the probabilitythat James is a drug user is 0.37. They consider barring him fromathletics. The real "monetary" values of the outcomes are difficultto assess in this case and, therefore, the value of each outcome isexpressed in a funny money unit: Galleon (from Harry PotterMovies). The following are the payoffs for the potentialoutcomes:Correctly identifying a drug user and barring this person fromathletics: 40 GalleonFalsely accusing a nonuser and barring this person fromathletics: -60 GalleonNot identifying a drug user and allowing this person toparticipate in athletics: -30 GalleonNot barring a nonuser: 0 GalleonBefore they make the decision, they can ask for a drug test,which costs -1 Galleon per single athlete . In the drug testing,assume there are two possible test results: positive and negative.For a drug user, the probabilities of these outcomes are 0.95 and0.05, respectively. For a nonuser, they are 0.01 and 0.99,respectively. Assume that 2% of all college athletes are drugusers.(When you use the probabilities from the flipped table, use cellreferences in the decision tree instead of typing the probabilitiesmanually. All choices in the following questions are based on thedecision tree built using this practice.)Question 5 (1 point)What is the EMV of making the decision without the test?A -58.6B -24C -12.1D -11.1Question 6 (1 point)If the first decision is to do the test or not and the seconddecision is to bar or not, what is the EMV of the whole tree? (Dueto the rounding error, your answer may not match perfectly with thecorrect choice. Pick the choice closest to your answer.)A -0.858B -0.269C 0.142D 2.678Question 7 (1 point)What is the best decision alternative?A Forgo the test and bar him.B Forgo the test and do not bar him.C Take the test. Bar him if the result is positive; do not barhim if the result is negative.D Take the test, and do not bar him.Question 8 (1 point)If the test costs -10 Galleon, what is the best decisionalternative?A Forgo the test and bar him.B Forgo the test and do not bar him.C Take the test. Bar him if the result is positive; do not barhim if the result is negative.D Take the test, and do not bar him.