# Joint-Probability

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To answer this question, I am supposed to utilize one or more of the following techniques.

-Confidence intervals and hypothesis testing

-Decision trees (and their use in solving managerial problems),

-Critical fractile analysis (and its use in determining optimal demand levels),

-Analysis of variance/ANOVA (and its use in understanding differences between group means),

-Chi-square (cross tabs/contingency table) analysis (and its use in determining differences between group proportions),

-Regression, single and multiple (and its use in understanding relationships between dependent and independent (explanatory) variables), and

-Optimization modeling (and its use in determining the best solution given a set of constraint).

Here is the question I am having trouble with:

The Petroski Company uses natural gas in its production-processing operations. Neighboring companies in the tristate area have successfully drilled for gas on their premises, and Petroski is considering following suit.

Their initial expenditure would be drilling, which would cost $80,000. If they strike gas, they would have to spend an additional $50,000 to cap the well and provide for the necessary hardware and control equipment. At the current price of natural gas, if the well is successful it will have a value of $750,000. However, if the price of gas rises to double its current value, a successful well will be worth $1,500,000. The company thinks its chance of finding gas is thirty percent (30%); it also believes that there is a 50 percent chance that the price of gas will double. What should the company do?

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##### Solution Summary

To answer this question, I am supposed to utilize one or more of the following techniques.

-Confidence intervals and hypothesis testing

-Decision trees (and their use in solving managerial problems),

-Critical fractile analysis (and its use in determining optimal demand levels),

-Analysis of variance/ANOVA (and its use in understanding differences between group means),

-Chi-square (cross tabs/contingency table) analysis (and its use in determining differences between group proportions),

-Regression, single and multiple (and its use in understanding relationships between dependent and independent (explanatory) variables), and

-Optimization modeling (and its use in determining the best solution given a set of constraint).

Here is the question I am having trouble with:

The Petroski Company uses natural gas in its production-processing operations. Neighboring companies in the tristate area have successfully drilled for gas on their premises, and Petroski is considering following suit.

Their initial expenditure would be drilling, which would cost $80,000. If they strike gas, they would have to spend an additional $50,000 to cap the well and provide for the necessary hardware and control equipment. At the current price of natural gas, if the well is successful it will have a value of $750,000. However, if the price of gas rises to double its current value, a successful well will be worth $1,500,000. The company thinks its chance of finding gas is thirty percent (30%); it also believes that there is a 50 percent chance that the price of gas will double. What should the company do?

##### Solution Preview

The company is facing two cases:

<br><br>1. whether the well is successful or not?

<br><br>cases: success unsucces

<br><br>Probability 0.3 0.7

<br><br>2. whether the price will double?

<br><br>cases: price double not double

<br><br>Probability 0.5 ...

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