Question 1

Please note --126,000 wrong answer. can you please provide answer with explanation

A local energy provider offers a landowner $180,000 for the exploration rights to natural gas on a certain site and the option for future development. This option, if exercised, is worth an additional $1,800,000 to the landowner, but this will occur only if natural gas is discovered during the exploration phase. The landowner, believing that the energy company's interest in the site is a good indication that gas is present, is tempted to develop the field herself. To do so, she must contract with local experts in natural gas exploration and development. The initial cost for such a contract is $300,000, which is lost forever if no gas is found on the site. If gas is discovered, however, the landowner expects to earn a net profit of $6,090,900. The landowner estimates the probability of finding gas on this site to be 60%%. Suppose now that, at a cost of $90,090, the landowner can request a soundings test on the site where natural gas is believed to be present. The company that conducts the soundings concedes that the test has a 30% false-negative rate (It indicates no gas when gas is present) and a 10% false positive rate (it indicates gas when no gas is prevent). a. If the landowner pays for the soundings test and the test indicates that gas is present, what is the landowner's revised probability that the site contains gas? Round your answer to three decimal places, if necessary. 0.91 b. If the landowner pays for the soundings test and the test indicates that gas is not present, what is the landowner's revised probability that there is no gas on the site7 Round your answer to three decimal places, If necessary. 0.667 c. Should the landowner request the soundings test at a cost of $90,000? No , because the sounding test is worth $ 126000Two construction companies are bidding against one another for the right to construct a new community center building. The first construction company, Fine Line Homes, believes that its competitor, Buffalo Valley Construction, will place a bid for this project according to the distribution shown in this table: Buffalo Valley's Bid Bid Probability $160,000 0.3 $165,000 0.4 $170,000 0.2 $175,000 0.1 Furthermore, Fine Line Homes estimates that it will cost $160,090 for its own company to construct this building. Given its fine reputation and long-standing service within the local community, Fine Line Homes believes that it will likely be awarded the project in the event that it and Buffalo Valley Construction submit exactly the same bids, Find the bid that maximizes Fine Line's expected profit. Max expected profit $ 165500 Bid that maximizes profit $ 170000 Is a decision tree really necessary? Explain your answer. This is an example of a one-stage decision problem where a payoff table is easier to create than a decision tree