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
a. Answer the question based on your
own feelings.
b. Answer the question using mathematical
expectation as a basis for selecting
your answer.
c. Conduct a survey of at least 10
people and summarize your results.
d. What are the conclusions of the
study.
a. Choose between A and B:
A. A sure gain of $240
B. 25% chance to gain $1,000
and 75% chance to gain $0
b. Choose between C and D:
C. A sure loss of $700
D. 75% chance to lose $1,000
and 25% chance to lose nothing
c. Choose between E and F:
E. 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?
F. 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?
d. Answer each of the questions based on your
own feelings.
e. Answer questions a and b using mathematical
expectation as a basis for
selecting your answers.
f. Conduct a survey of at least 10 people
and summarize your results.a. 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.
