# Probability & QM - pls check whether my answers are correct

Questions
1. National Oil Company conducts exploratory oil drilling operations in the south western United States. To fund the operation, investors form partnerships, which provide the financial support necessary to drill a fixed number of oil wells. Each well drilled is classified as a producer well or a dry well. Past experience shows that 15% of all wells drilled are producer wells. A newly formed partnership has provided the financial support for drilling at 12 exploratory locations.

1.What is the probability that all 12 wells will be producer wells?

We have to find the probability of all the 12 wells drilled are producer wells with a 15% prior probability. Here we will calculate the probability using binomial distribution method.
The formula is
P(k out of n) =[n!/k!(n-k)! ](p^k)(q^n-k)
where k =12, number of times a producer well drilled, p = 15% or .15 is the observed probability of a producer well , q = 85% or .85 is the complementary probability (1-p) that is of a dry well, and n = 12 is the number of wells drilled.
Substituted as
P(12 12) =[479001600/479001600(1)](.1512)(.851)
P=0.000000000129746337890625
We can observe that the chances of finding all 12 wells as producer wells are approximately nill.

2.What is the probability that all 12 wells will be dry wells?

Here, we will find the probability of all the 12 wells drilled are dry wells with 85% prior probability.
k =12, number of times a dry well drilled, p = 85% or .85 is the observed probability of a dry well , q = 15% or .15 is the complementary probability (1-p) that is of a producer well, and n = 12 is the number of wells drilled.
Substituted as
P(12 out of 12) =[479001600/479001600(1)](.8512)(.151)
P=0.142241757136172119140625
We can observe a 14.2% chance of finding all 12 wells as dry wells.

3.What is the probability that exactly one well will be a producer well?

k =1, number of times a producer well drilled, p = 15% or .15 is the observed probability of a producer well , q = 85% or .85 is the complementary probability (1-p) that is of a dry well, and n = 12 is the number of wells drilled.
Substituted as
P(1/12) =[479001600/1(39916800)](.151)(.8511)
P = 12 (.15)(0.1673432436896142578125)
P=0.3012178386413056640625

Here we can observe that the chances of finding exactly 1 producer well out of 12 wells drilled is approximately 30%.

thanks

HallsofIvy
Homework Helper
Questions
1. National Oil Company conducts exploratory oil drilling operations in the south western United States. To fund the operation, investors form partnerships, which provide the financial support necessary to drill a fixed number of oil wells. Each well drilled is classified as a producer well or a dry well. Past experience shows that 15% of all wells drilled are producer wells. A newly formed partnership has provided the financial support for drilling at 12 exploratory locations.

1.What is the probability that all 12 wells will be producer wells?

We have to find the probability of all the 12 wells drilled are producer wells with a 15% prior probability. Here we will calculate the probability using binomial distribution method.
The formula is
P(k out of n) =[n!/k!(n-k)! ](p^k)(q^n-k)
where k =12, number of times a producer well drilled, p = 15% or .15 is the observed probability of a producer well , q = 85% or .85 is the complementary probability (1-p) that is of a dry well, and n = 12 is the number of wells drilled.
Substituted as
P(12 12) =[479001600/479001600(1)](.1512)(.851)
P=0.000000000129746337890625
We can observe that the chances of finding all 12 wells as producer wells are approximately nill.
(.15^12)(.85^0), not "(.1512)(.851) (and certainly not that last "1"!). Since your probabilties were only give to 2 decimal places, keeping 15 significant figures is misleading: P= 1.30 x 10^(-10) would be better.
(And I don't believe that "approximately nil" is a mathematical term!)

2.What is the probability that all 12 wells will be dry wells?

Here, we will find the probability of all the 12 wells drilled are dry wells with 85% prior probability.
k =12, number of times a dry well drilled, p = 85% or .85 is the observed probability of a dry well , q = 15% or .15 is the complementary probability (1-p) that is of a producer well, and n = 12 is the number of wells drilled.
Substituted as
P(12 out of 12) =[479001600/479001600(1)](.8512)(.151)
P=0.142241757136172119140625
We can observe a 14.2% chance of finding all 12 wells as dry wells.
Same comments as above: You mean (.85^12)(.15^0). I would have said "a 14% chance" since your original probabilities were given to the nearest percent.

3.What is the probability that exactly one well will be a producer well?

k =1, number of times a producer well drilled, p = 15% or .15 is the observed probability of a producer well , q = 85% or .85 is the complementary probability (1-p) that is of a dry well, and n = 12 is the number of wells drilled.
Substituted as
P(1/12) =[479001600/1(39916800)](.151)(.8511)
P = 12 (.15)(0.1673432436896142578125)
P=0.3012178386413056640625

Here we can observe that the chances of finding exactly 1 producer well out of 12 wells drilled is approximately 30%.[/B
thanks

Again, you mean (.15^1)(.85^11)- but now the "1" is correct!

hi HallsofIvy

missing carets and others were copy paste errors.

thanks for your help and suggestions

also Prof. HallsofIvy,

I have couple of sets of problems that i have solved which needs to be commented. Can I post those?
Iam in IT profession and doing my MBA in info systems.
thanks

HallsofIvy
Homework Helper
You are welcome to post as long as you abide by forum rules: Make an effort to do them yourself and post your work.

probability questions & solutions

hi professor

questions and my answers are attached as pdf file.
pls comment.

thanks a lot

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