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**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.

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.

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%.

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

thanks