Individual Research Projects Section 13.2

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Project 13.3

The questions in this problem are from a study by MacCrimmon, Stanbury, and Wehrung, “Real Money Lotteries: A Study of Ideal Risk, Context Effects, and Simple Processes,” in Cognitive Processes in Choice and Decision Behavior, edited by Thomas Wallsten, (Hillsdale, N. J.: Lawrence Erlbaum Associates, 1980, pp. 155-179).

Question: You have five alternatives from which to choose. List your preferences for the alternatives from best to worst.

  1. sure win of $5 and no chance of loss
  2. 6.92% chance to win $20 and 93.08% chance to win $3.98
  3. 27.52% chance to win $20 and 72.48% chance to lose 69 cents
  4. 61.85% chance to win $20 and 38.15% chance to lose $19.31
  5. 90.46% chance to win $20 and 9.54% chance to lose $137.20
    1. Answer the question based on your own feelings.
    2. Answer the question using mathematical expectation as a basis for selecting
      your answer.
    3. Conduct a survey of at least 10 people and summarize your results.
    4. What are the conclusions of the study.

 

Project 13.4

  1. Choose between A and B:
    1. A sure gain of $240
    2. 25% chance to gain $1,000 and 75% chance to gain $0
  2. Choose between C and D:
    1. A sure loss of $700
    2. 75% chance to lose $1,000 and 25% chance to lose nothing
  3. Choose between E and F:
    1. Imagine that you have decided to see a concert and have paid the admission price of $10. As you enter the concert hall, you discover that you have lost your ticket. Would you pay $10 for another ticket?
    2. Imagine that you have decided to see a concert where the admission is $10. As you begin to enter the concert ticket line, you discover that you have lost one of your $10 bills. Would you still pay $10 for a ticket to the concert?
  4. Answer each of the questions based on your own feelings.
  5. Answer questions a and b using mathematical expectation as a basis for selecting your answers.
  6. Conduct a survey of at least 10 people and summarize your results. Answer each of the following questions* based on your own feelings.

* These questions are from A Bird in the Hand, by Carolyn Richbart and Lynn Richbart in The Mathematics Teacher, November 1996, pp. 674-676.