Question

After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are as follows.
P(soil | high-quality oil) = 0.20 P(soil | medium-quality oil) =0.80 P(soil | no oil) = 0.20
How should the firm interpret the soil test? What are the revised probabilities?
Events P(Ai) P(S | Ai) P(Ai∩S) P(AiS)
High Quality (A1)
Medium Quality (A2)
No Oil (A3) P(S)=
What is the new probability of finding oil?

Answer 1

The firm can interpret the soil test by using Bayes’ Theorem to see what the posterior probabilities of seeing different of oil as wlel as no oil are. By using this, you can tell that it’s more likely that they are going to find medium quality oil.

P(E1soil)= .5*.2=.1

P(E2 soil)=.2*.8=.16

P(E3soil)=.3*.2=.06

P(soil)=.1+.16+.06=.32

P(E1|soil)=.1/.32=.3125

P(E2|soil)=.16/.32=.5

P(E3|soil)=.06/.32=.1875

P(Oil)=P(medium quality oil high quality oil)=.3125+.5=.81257

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great rest of Black History Month! :-)  

- Cutiepatutie ☺❀❤