SOLUTION: An oil drilling company is considering 2 sites for its well. The probabilities for getting a dry, a low-producing, or a high-producing well at site A are 0.6, 0.25, and 0.15, respe

Question 1201804: An oil drilling company is considering 2 sites for its well. The probabilities for getting a dry, a low-producing, or a high-producing well at site A are 0.6, 0.25, and 0.15, respectively. The costs for the 3 eventualities are −$300,000, $450,000, and $1,500,000.
For site B, the probability of finding a dry well, resulting in a $240,000 loss, is 0.2. The company estimates that the probability of a low-producing well is 0.8, and in that case it would make $60,000.
(Part 1:) Make a tree diagram for this situation and find the expected value for site A.
(Part 2:) Find the expected value for site B.

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Thank you!
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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An oil drilling company is considering 2 sites for its well.
The probabilities for getting a dry, a low-producing, or a high-producing well at site A are
0.6, 0.25, and 0.15, respectively.
The costs for the 3 eventualities are −$300,000, $450,000, and $1,500,000.
For site B, the probability of finding a dry well, resulting in a $240,000 loss, is 0.2.
The company estimates that the probability of a low-producing well is 0.8,
and in that case it would make $60,000.
(Part 1:) Make a tree diagram for this situation and find the expected value for site A.
(Part 2:) Find the expected value for site B.
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                                        Part 1


For site A, there are 3 possible outcomes with described probabilities and costs.

So, the expected value for site A is the sum of three addends

    expected value for site A = 0.6*(-300000) + 0.25*450000 + 0.15*1500000 = 157500  dollars.


                                        Part 2


For site B, there are 2 possible outcomes with described probabilities and costs.

So, the expected value for site B is the sum of two addends

    expected value for site A = 0.2*(-240000) + 0.8*60000 = 0  dollars.

Solved.

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If you want to see other similar (and different) solved problems on Mathematical expectation
to make your horizon wider, look in the lessons
    - Math expectation of winning in games problems
    - Math expectation of winning in lottery problems
    - Math expectation of winning in games with rolling pair of dice
in this site.

Learn the subject from there ( ! )

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