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

I. Sure win of \(\$ 5\) and no chance of loss II. \(6.92 \%\) chance to win \(\$ 20\) and \(93.08 \%\) chance to win \(\$ 3.98\)

III. \(27.52 \%\) chance to win \(\$ 20\) and \(72.48 \%\) chance to lose 69 cents IV. \(61.85 \%\) chance to win \(\$ 20\) and \(38.15 \%\) chance to lose \(\$ 19.31\)

V. \(90.46 \%\) 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?