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# New Source, Inc. - Probability

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NewSource Inc. uses natural gas in its production-processing operations. Neighboring companies in its upstate Ohio area have successfully drilled for gas on their premises, and NewSource 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; it also believes that there is a 50 percent chance that the price of gas will double. What should the company do?

##### Solution Summary

The solution discusses NewSource Inc. uses natural gas in its production-processing operations. Neighboring companies in its upstate Ohio area have successfully drilled for gas on their premises, and NewSource 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; it also believes that there is a 50 percent chance that the price of gas will double. What should the company do?

##### Solution Preview

Let F be the event that gas is "Found".
Let D be the event the gas prices "Double".
We assume these two events are independent.
So, there are four outcomes in the sample space:
{-F-D, -FD, F-D, FD}.
We are given that the probability of finding gas is
p(F) = .3
and that the probability of the price of gas doubling is
p(D) = .5

So, the probability of not finding gas is
p(-F) = 1 - .3 = .7
and the probability of the price of gas not doubling is
p(-D) = 1 - .5 = .5

Since it seems reasonable that events of finding gas and the price doubling are ...

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