1 An oil company purchased an option on land in Alaska Preli

1. An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.

P(find high quality oil) = 0.50

P(find medium quality oil) = 0.20

P(find no oil) = 0.30

After 200 feet of drilling on the first well, a soil test is made. The probabilities of finding a special type of soil (i.e. soil XYZ) identified by the tests are

P(find soil XYZ | find high quality oil) = 0.30

P(find soil XYZ | find medium quality oil) = 0.50

P(find soil XYZ | find no oil) = 0.20

a. What is the probability of finding oil?

b. What is the probability of finding soil XYZ?

c. What is the probability of finding oil given that soil XYZ is found in the test?

Please show work! Thanks

Solution

P(H) = 0.50

P(M) = 0.20

P(N) = 0.30

After 200 feet of drilling on the first well, a soil test is made. The probabilities of finding a special type of soil (i.e. soil XYZ) identified by the tests are

P(XYZ / H) = 0.30

P(XYZ / M) = 0.5

P(XYZ / N) = 0.20

P(XYZ) = P(XYZ / H)P(H) + P(XYZ / M)P(MO)+ P(XYZ / N)P(N)

P(XYZ) = 0.30*0.5 + 0.50*0.20+0.2*0.30

P(XYZ) = 0.31

P(H/ XYZ) = P(XYZ/H)P(H) / P(XYZ) = 0.30*0.50 / 0.31 = 0.4838

P(M/XYZ) = P(XYZ/M)P(M)/P(XYZ) = 0..50*0.20 / 0.31 = 0.3225

P(N/XYZ) = P(XYZ/N)P(N)/P(XYZ) = 0.20*0.30 / 0.31 = 0.1935