### 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.

- sure win of $5 and no chance of loss
- 6.92% chance to win $20 and 93.08% chance to win $3.98
- 27.52% chance to win $20 and 72.48% chance to lose 69 cents
- 61.85% chance to win $20 and 38.15% chance to lose $19.31
- 90.46% chance to win $20 and 9.54% chance to lose $137.20
- Answer the question based on your own feelings.
- Answer the question using mathematical expectation as a basis for selecting

your answer. - Conduct a survey of at least 10 people and summarize your results.
- What are the conclusions of the study.

### Project 13.4

- Choose between A and B:
- A sure gain of $240
- 25% chance to gain $1,000 and 75% chance to gain $0

- Choose between C and D:
- A sure loss of $700
- 75% chance to lose $1,000 and 25% chance to lose nothing

- Choose between E and F:
- 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?
- 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?

- Answer each of the questions based on your own feelings.
- Answer questions a and b using mathematical expectation as a basis for selecting your answers.
- 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.