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A collector is considering whether to buy a painting. The painting has a list price of $5000, but it could be worth $10,000 if it is not a counterfeit. It will be worth nothing if it is a fake.
A) Draw the decision tree. The collector things there is a 60-40 odds that the painting is not fake.
B) Suppose now some appraiser can identify the painting with 90% if its not a counterfeit, and 80% if it is a counterfeit. If the appraiser chargers $500 for consultation, should the collector pay the consultation fee and ask for consultation? My teacher did the problem in class but the next day said he was wrong but I do not know where he was wrong or what to change. This is what he gave in class the first day that turned out to be wrong. After drawing the decision tree. P(real)*P("real"|real) / P("real"|real)+P("real"|fake)*P(fake) Which he got to be (.6*.9)/(.6*.9+.4*.2) = .87 Expected Value with info = .6[.8*.87*5000+.13*-5000] + .4*0 =2200 I emailed him asking what to do with the new number he gave in class and he said "The answer is basically about the same, you just replace .6 with .62 in the calculation and replace .4 with .38" Can someone please explain to me what to do? And what the formula he used to get .87 is and is used for?
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