Jnb/ievonde htmildeploymented-57360111313537361057776297813373985908 3248811 MIN

Question

Jnb/ievonde htmildeploymented-57360111313537361057776297813373985908 3248811 MINDTAP Search thes course gnment: Chapter 4 Assignment tions Esercise 04.5 ution 3 of Check My Work oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the followling prior probabliies P(high-quality oil)- .4 P(medium-quality ol)- 04 Pno oil)0.2 a. what is the probablity of finding oll (to 1 dedmal? b. After 200 feet of drilling on the first well, a soll test is taken. The probabilibies of finding the partioular type of soll identified by the test are given below P(sollmedion-quality oil)-.5 Pisoino oil)0.2 Given the sall found in the best, use Bayes theorem to comoube the folowing nevised probabilities te4 dema) P(high-quality oilhoil) Pinedium-quality oll od)3 What is the new peobability of inding oill to 4 decimals 0 AYUNDAI

Explanation / Answer

Probability of finding oil = P(high-quality oil) + P(medium-quality oil)

= 0.4+0.4

=0.8

Using Bayes Theorem

P(high-qualty oil | soil)= [P(soil | high-quality oil) x P(high-quality oil)] / P(soil)

P(medium-qualty oil | soil)= [P(soil | medium-quality oil) x P(medium-quality oil)] / P(soil)

P(no oil | soil)= [P(soil | no oil) x P(no oil)] / P(soil)

P(soil) = 0.4x0.3 + 0.4x0.5 + 0.2x0.2

= 0.36

P(high-qualty oil | soil) = 0.4x0.3/0.36

=0.3333

P(medium-qualty oil | soil)= 0.4x0.5/0.36

=0.5556

P(no oil | soil)= 0.2x0.2/0.36

=0.1111

New Probability of finding oil= 0.3333+0.5556=0.8889

As probability of finding medium quality oil is greatest (0.5556) it is most likely to be found.

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