ldMal-ellie deBA2300-Sylab x Cengage O Not secure ng.cengage.com/static/nb/ui/in

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ldMal-ellie deBA2300-Sylab x Cengage O Not secure ng.cengage.com/static/nb/ui/indexh AP ssignment tml?nbld 7156698nbNodeld-2693750738elSBN-9781337115377parentld-269375302 11 PM EST eBook An oil company purchased an option on lan d in Alaska. Preliminary geologic studies assigned the following prior probabilities. P(high-quality oil) 0.3 P(medium-quality oil) 0.5 Pino oil) 0.2 a. What is the probability of finding oil (to 1 decimal)? b. Ater 200 fet of diling on the fist well, a oil test s taken. The probabilties of finding the particular type of soil dentified by the test are given below. P(soil!high-quality oil) Pisoilmediurn-quality oil) P(soil no oil) 0.4 0.4 0.2 Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals) P(high-quality oil soil) P(medium-quality oil soil) P(no oillsoil) What is the new probability of finding oil (to 4 decimals)? According to the revised probabilities, what is the quality of oil that is most likely to be found? Select your answer - O Icon Key O Type here to search e@a«I

Explanation / Answer

a) P(Finding Oil) = 0.3 + 0.5 = 0.8

b) P(High quality oil |soil) = (0.4*0.3)/(0.4*0.3 + 0.4*0.5 + 0.2*0.2) = 0.3333

P(Medium quality oil | Soil) = (0.4*0.3)/(0.4*0.3 + 0.4*0.5 + 0.2*0.2) = 0.5556

P(No oil | Soil) = (0.2*0.2)/(0.4*0.3 + 0.4*0.5 + 0.2*0.2) = 0.1111

c) P(Finding oil) = 0.3*0.4 + 0.5*0.4 + 0.2*0.2 = 0.36

Medium quality oil is most likely to be found.

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