An oil company has selected a site to drill for a well. The site was chosen beca
ID: 3224101 • Letter: A
Question
An oil company has selected a site to drill for a well. The site was chosen because the company thought there might be a dome structure, a shale formation deep in the ground that often presages the presence of oil. Based on geological survey information, the company geologist has assessed the probability of a dome structure at 0.4. Past data and geological information have led the geologist to estimate the probability of a major oil strike at 0.2 if there is a dome formation and 0.1 if there is not. If there is no major oil strike, there could still be a small; the probabilities of a small oil strike have been estimated at 0.5 if there is a dome and 0.2 if there is not. The only other possibility is no oil. Given these prior probabilities determine the probability of there having been a dome if there is (a) a major strike; (b) a small strike; (c) no oil.
Explanation / Answer
probability of drome = 0.4
probability of oil strike if dome is there = 0.2
probability of oil strike if dome is not there = 0.2
probability of small oil strike if dome is there = 0.5
probability of small oil strike if dome is not there = 0.2
a)
the probability of there having been a dome if there is a major strike :
the probability of a major strike with dome present = 0.4*0.2 = 0.08
the probability of a major strike with dome present = 0.6 * 0.1 = 0.06
thus probability of there having been a dome if there is a major strike = 0.08 / (0.08 + 0.06) =0.5714
b)
the probability of there having been a dome if there is a small strike :
the probability of a small strike with dome present = 0.4 * 0.8 * 0.5 = 0.16
the probability of a small strike with dome present = 0.6 * 0.9 * 0.2 = 0.108
thus probability of there having been a dome if there is a small strike = 0.16 / (0.108 + 0.16) =0.597
c)
the probability of there having been a dome if there is a no strike :
the probability of a no strike with dome present = 0.4 * 0.8 * 0.5 = 0.16
the probability of a no strike with dome present = 0.6 * 0.9 * 0.8 = 0.432
thus probability of there having been a dome if there is a small strike = 0.16 / (0.432 + 0.16) = 0.2702