Help!! Probability ?????????????

I have a problem and need some step to step computation and a bit of explanantion. Have deadine of tomorrow

Here's the problem:
Oil company purchase land in Alaska..Preliminary geograhic studies assigned the following:

P(high-quality oil) = .50
P(medium -quality oil) .20
P(no oil) = .30

(a) What is the probaility of finding oil ?
(b) 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 follow.

p(soil /high quality oil) = .20
p(soil/medium-quality oil) = .80
P(soil/no oil) = .20

How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding the oil?

HELP PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!



TS Contributor

What have you attempted so far?

For part (a), it is simply = 1 - P(no oil).

For part (b), this looks like a situation for Bayes formula, i.e.,

the revised probabilities would be:

P(high-quality oil | soil)
P(medium-quality oil | soil)
P(no oil | soil)


Thank you for responding!

I haven't attempt the problem. I was out sick for this day of class and my tutoring session is not schedule until next week, but I need to understand and do this problem in order to move ahead to the next problems. I read the problem and thought that, they did not give me enough information to complete it.

Yes, part (b) we are suppose to use Bayes theorem!

For clarification:

For Part A, How would I show I show it as a fraction!
Would it be 1-.30 = .7[/B]

For Part B, How would I apply Bayes theorem!



TS Contributor
for part (a), you could just report it as 0.7 or 7/10

for part (b), Bayes formula is:

event A = particular type of soil
event B = particular type of oil

P(B|A) = P(A|B)*P(B) / [ P(A|B)*P(B) + P(A|B')*P(B') ]

What Bayes' formula does is it modifies or revises the probability of the occurrence of an event, based on "additional" information. Originally, the probability of high-quality oil was tought to be 0.5. Then they took a soil sample 200 feet down, and this is the "additional" information. You are asked to determine how this additional information revises the probability of an event.
Good Morning:

John I attempt to use Bayes theorem last night in finding the new probability of oil. Can you verify if I calculated this correctly?

I use .20 for (A) and .80 for B

Using Bayes formula I calculate it as 1.0 x .80 / 1.0 x .80 + 1.0 x .80 = 1.44

No sure if this is done right!

Good morning Elizer,

In the denominator of the Bayes formula, you have P(A|B)*P(B) + P(A|B')*P(B'), the second part is different from the first part. B' is the complement of B, P(B')=1-P(B).
Thank you for the explanantion: So can you tell me if I calulate it correctly!

For P(A/B') would be 1-.80(A) = .20(B). so then I inputted the information into the formula as:

1.0 x .80 / 1.0 x .80 + .40 x .20 = .72

I am due to attend class in the next 15 minutes
I still did not get it because the first problem identify no oil as 030, but then addt information was given and teh probabilities change. So I thought I would be working from the second set of new probabilities.
P(high-quality oil | soil) = p(soil /high quality oil)*p(high quality oil) /[p(soil /high quality oil)*p(high quality oil) + p(soil /medium quality oil)*p(medium quality oil) +p(soil /no oil)*p(no oil)]
=.20*.50/[.20*.50 + .80*.20 + .20*.30]

My first post was a general comment regarding Bayes theorem. There are three groups in your problem, so you need to use all three groups.