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Chapter 9: Problem 3

A big private oil company must decide whether to drill in the Gulf of Mexico. It costs \(\$ 1\) million to drill, and if oil is found its value is estimated at \(\$ 6\) million. At present, the oil company believes that there is a \(45 \%\) chance that oil is present. Before drilling begins, the big private oil company can hire a geologist for \(\$ 100,000\) to obtain samples and test for oil. There is only about a \(60 \%\) chance that the geologist will issue a favorable report. Given that the geologist does issue a favorable report, there is an \(85 \%\) chance that there is oil. Given an unfavorable report, there is a \(22 \%\) chance that there is oil. Determine what the big private oil company should do.

Short Answer

Expert verified
Hire the geologist and then drill if the report is favorable.

Step by step solution

01

Understanding the Problem

The oil company needs to decide whether to spend money on drilling based on initial probabilities of finding oil and improve these estimates by hiring a geologist. The costs and potential rewards must be weighed against these probabilities.
02

Calculating Expected Value without Geologist

The expected monetary outcome without hiring a geologist is calculated based on the probability of finding oil (45%). If oil is found, the company gains \(6 million, but they incur a \)1 million drilling cost regardless.\[ \text{Expected Value}_{\text{without geologist}} = (0.45 \times (6 - 1)) + (0.55 \times (-1)) \]This simplifies to:\[ (0.45 \times 5) + (0.55 \times -1) = 2.25 - 0.55 = 1.7 \text{ million dollars} \]
03

Calculating Expected Value with Geologist - Favorable Report

If the geologist provides a favorable report, the probability of finding oil increases to 85%. The calculation is modified accordingly. The geologist charges $100,000 upfront.\[ \text{Expected Value}_{\text{favorable}} = (0.85 \times (6 - 1 - 0.1)) + (0.15 \times (-1 - 0.1)) \]This simplifies to:\[ 0.85 \times 4.9 + 0.15 \times -1.1 = 4.165 - 0.165 = 4 \text{ million dollars}\]
04

Calculating Expected Value with Geologist - Unfavorable Report

If an unfavorable report is issued, there is still a 22% chance of finding oil, but less likely than the initial belief. Expected value is recalculated:\[ \text{Expected Value}_{\text{unfavorable}} = (0.22 \times (6 - 1 - 0.1)) + (0.78 \times (-1 - 0.1)) \]This simplifies to:\[ 0.22 \times 4.9 + 0.78 \times -1.1 = 1.078 - 0.858 = 0.22 \text{ million dollars} \]
05

Average Expected Value with Geologist

Given a 60% probability of a favorable report and a 40% probability of an unfavorable report, the overall expected value when hiring a geologist can be computed:\[ \text{Average Expected Value}_{\text{with geologist}} = (0.6 \times 4) + (0.4 \times 0.22) \]This simplifies to:\[ 2.4 + 0.088 = 2.488 \text{ million dollars} \]
06

Decision Making

The expected value when hiring a geologist (2.488 million dollars) is higher than the expected value without hiring a geologist (1.7 million dollars). Hence, the company should hire the geologist before deciding to drill.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Expected Value
Expected value is an important concept in decision analysis. It helps in predicting the potential outcomes of uncertain events. You can think of expected value as the average result you would expect if the scenario occurred an infinite number of times.
When the oil company evaluates whether to drill, they initially calculate the expected value without hiring a geologist. This involves multiplying the probabilities of each outcome by their respective financial gains or losses. For example, there is a 45% chance of finding oil, resulting in an expected gain of 5 million dollars after deducting the drilling cost. The calculation for expected value without hiring the geologist is:
  • Probability of finding oil: 0.45
  • Value if oil is found: 6 million dollars - 1 million dollar cost = 5 million dollars
  • Expected value (without geologist): \[ (0.45 \times 5) + (0.55 \times -1) = 1.7 \text{ million dollars} \]
Incorporating expected value helps the company weigh their options financially before making a decision.
Probability
Probability plays a crucial role in analyzing uncertain events, like the likelihood of finding oil in this scenario. It helps the company make informed decisions. Understanding probability allows them to assess risks and determine the most financially sensible path.
In the exercise, several probability values are crucial:
  • 45% chance of finding oil without geologist.
  • 85% chance of oil if the report from the geologist is favorable.
  • 22% chance of oil if the geologist's report is unfavorable.
The geologist's report can dramatically shift the probabilities. If favorable at 85%, the likelihood improves significantly, affecting the decision-making process. This change in probabilities directly impacts the expected value calculation and the final decision.
Cost-Benefit Analysis
Cost-benefit analysis is essential for making smart business decisions, especially in risky ventures. For the oil company, this involves comparing the costs of drilling against the potential financial gains.
Here's how the exercise employs cost-benefit analysis:
  • The company spends 1 million dollars on drilling, and potentially gains 6 million dollars if oil is found.
  • Hiring a geologist costs 100,000 dollars, but can significantly influence the probability of finding oil.
By evaluating both expected values鈥攐ne with and one without the geologist's input鈥攖he company performs a cost-benefit analysis to determine which scenario offers a more substantial financial return. The future decision to drill is based on the higher expected value of 2.488 million dollars when involving the geologist. The analysis thus ensures that they are making a data-driven and financially reliable choice.

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Most popular questions from this chapter

Refer to the rolling of a pair of dice example. Determine the probability of rolling a 7 or an 11 . If you roll a 7 or 11 , you win \(\$ 5\), but if you roll any other number, you lose \(\$ 1\). Determine the expected value of the game.

The number of attempts to use an ATM per person per month and their probabilities are listed in the following table. Compute the expected value and interpret that value. Discuss how similar calculations could be used to determine the number of ATMs needed. $$ \begin{array}{lllll} \hline \text { Attempts } & 1 & 2 & 3 & 4 \\ \text { Probability } & 0.5 & 0.33 & 0.10 & 0.07 \\ \hline \end{array} $$

We are considering one of three alternatives A, B, or C under uncertain conditions. The payoff matrix is as follows: $$ \begin{array}{lccc} \hline & {\text { Conditions }} \\ \text { Alternative } & 1 & 2 & 3 \\ \hline \text { A } & 3000 & 4500 & 6000 \\ \text { B } & 1000 & 9000 & 2000 \\ \text { C } & 4500 & 4000 & 3500 \\ \hline \end{array} $$ Determine the best plan by each of the following criteria and show your work: a. Laplace b. Maximin c. Maximax d. Coefficient of optimism (assume that \(x=0.65\) ) e. Regret (minimax)

We have engaged in a business venture. Assume the probability of success is \(P(s)=2 / 5 ;\) further assume that if we are successful we make \(\$ 55,000\), and if we are unsuccessful we lose \(\$ 1750\). Find the expected value of the business venture.

A local TV studio is deciding on a possible new TV show. A successful TV show earns the station about \(\$ 450,000, but if it is not successful, the station loses about \)\$ 150,000 . Of the previous 100 shows reviewed by the local TV station, 25 turned out to be successful TV shows, and 75 turned out to be unsuccessful TV shows. For a cost of \(\$ 45,000, the local station can hire Buddy's Market Research team; this team will use a live audience in previewing the TV pilots to determine whether the viewed TV show will be successful. Past records show that market research predicts a successful TV show about \)90 \%\( of the time that the TV show was actually successful and predicts an unsuccessful show \)80 \%$ of the time that it turned out to be unsuccessful. How should the local TV studio maximize its profits?
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