# Individual Research Projects Section 13.2

### 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.