Practice and Application Exercises 5. An architect is considering bidding for the design of a new museum. The cost of drawing plans and submitting a model In Exercises 1-2, the numbers that each pointer can land on and is $10,000. The probability of being awarded the bid is 0.1, their respective probabilities are shown Compute the expected and anticipated profits are $100,000, resulting in a possible value for the number on which each pointer lands. gain of this amount minus the $10,000 cost for plans and a 1. Outcome Probability model. What is the expected value in this situation? Describe what this value means. 1 NIH 6. A construction company is planning to bid on a building 2 contract. The bid costs the company $1500. The probability that the bid is accepted is 3. If the bid is accepted, the 3 company will make $40,000 minus the cost of the bid. Find the expected value in this situation. Describe what this value means . 7. It is estimated that there are 27 deaths for every 10 million people who use airplanes. A company that sells flight insurance.provides $100,000 in case of death in a plane crash. Outcome Probability A policy can be purchased for $1. Calculate the expected value and thereby determine how much the insurance company can 1 make over the long run for each policy that it sells. 2 8. A 25-year-old can purchase a one-year life insurance policy for $10,000 at a cost of $100. Past history indicates that the 3 probability of a person dying at age 25 is 0.002. Determine 4 the company's expected gain per policy. Exercises 9-10 are related to the SAT, described in Check Point 4 on page 662. 9. Suppose that you can eliminate one of the possible five answers. Modify the two probabilities shown in the final The tables in Exercises 3-4 show claims and their probabilities for column in Table 11.12 on page 662 by finding the an insurance company. probabilities of guessing correctly and guessing incorrectly a. Calculate the expected value and describe what this means under these circumstances. What is the expected point value in practical terms. of a random guess? Is it advantageous to guess under these b. How much should the company charge as an average circumstances? premium so that it breaks even on its claim costs? 10. Suppose that you can eliminate two of the possible five c. How much should the company charge to make a profit of answers. Modify the two probabilities shown in the final $50 per policy? column in Table 11.12 on page 662 by finding the 3. PROBABILITIES FOR HOMEOWNERS' probabilities of guessing correctly and guessing incorrectly INSURANCE CLAIMS under these circumstances. What is the expected point value Amount of Claim (to the of a random guess? Is it advantageous to guess under these nearest $50,000) Probability circumstances? $0 0.65 11. A store specializing in mountain bikes is to open in one of $50,000 0.20 two malls. If the first mall is selected, the store anticipates a $100,000 0.10 yearly profit of $300,000 if successful and a yearly loss of $150,000 0.03 $100,000 otherwise. The probability of success is 7. If the $200,000 second mall is selected, it is estimated that the yearly profit 0.01 $250,000 will be $200,000 if successful; otherwise, the annual loss will 0.01 be $60,000. The probability of success at the second mall is a. 4. PROBABILITIES FOR MEDICAL INSURANCE Which mall should be chosen in order to maximize the CLAIMS expected profit? Amount of Claim (to the 12. An oil company is considering two sites on which to drill, nearest $20,000) Probability described as follows: $0 0.70 Site A: Profit if oil is found: $80 million $20,000 0.20 Loss if no oil is found: $10 million $40,000 0.06 Probability of finding oil: 0.2 $60,000 0.02 Site B: Profit if oil is found: $120 million $80,000 0.01 Loss if no oil is found: $18 million $100,000 0.01 Probability of finding oil: 0.1 Which site has the larger expected profit? By how much