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

#1
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 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Thanks
E
 

JohnM

TS Contributor
#2
Elizer,

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)
 
#3
Response

John:

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!

Thanks
E
 

JohnM

TS Contributor
#4
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.
 
#5
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!

Thanks
E
 
#6
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).
 
#7
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
 
#9
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.
 
#10
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.