Spring 2022 Computer Science 458

Assignments

The Realm of Decisions

You are in the market for a used car. Suppose that the value of a low-quality used car is $5,000 and the value of a high-quality car is $12,000. Suppose that you cannot distinguish with certainty the quality of the used car but you have 65 % information based on the Carfax that the used car you were willing to buy is of high quality. How much are you willing to pay for the used car?

Answer: The probability of you getting a high-quality used car is 0.65 which means the probability of you getting a low-quality used car is 1-0.65 = 0.35. You value a high-quality car at $12,500 and a low-quality car at $5,000. Thus, the expected value of the car is 0.65*12,500+0.35*5,000 = $9,875. This is also the maximum price you are willing to pay for the car.

Today's Questions

• Question 1. You are given a choice: (a) get $900 for certain, or (b) 90% chance to win $1,000 and 10% chance for nothing. What do you choose?

  https://pollev.com/slade You may also download the app to your phone. Use the "slade" poll id.

• Question 2. You are given a choice: (a) lose $900 for certain, or (b) 90% chance to lose $1,000 and 10% chance of losing nothing. What do you choose?

  https://pollev.com/slade

• Question 3. Linda is thirty-one years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations...The respondents are asked to rank in order of likelihood various scenarios: Linda is (1) an elementary school teacher, (2) active in the feminist movement, (3) a bank teller, (4) an insurance salesperson, or (5) a bank teller also active in the feminist movement.

  https://pollev.com/slade

• Question 4. An individual has been described by a neighbor as follows: “Steve is very shy and withdrawn, invariably helpful but with very little interest in people or in the world of reality. A meek and tidy soul, he has a need for order and structure, and a passion for detail.” Is Steve more likely to be a librarian or a farmer?

  https://pollev.com/slade

• Question 5. Participants were asked to choose between two treatments for 600 people affected by a deadly disease. Treatment A was predicted to result in 400 deaths, whereas treatment B had a 33% chance that no one would die but a 66% chance that everyone would die. This choice was then presented to participants either with positive framing, i.e. how many people would live, or with negative framing, i.e. how many people would die.

  Choice one: Either saves 200 lives, or a 33% chance of saving all 600 people, 66% possibility of saving no one.

  https://pollev.com/slade

  Choice two: 400 people will die or a 33% chance that no people will die, and 66% probability that all 600 will die.

  https://pollev.com/slade

• Question 6.

  Write down the last 2 digits of your Social Security number. Now consider whether you would pay this number of dollars for items whose value you do not know, such as wine, chocolate and computer equipment. Finally, how much are you willing to pay? (Enter two numbers)

  https://pollev.com/slade

• Getting a covid vaccine.