a. Choose between \(\mathrm{A}\) and \(\mathrm{B}\) :

A. A sure gain of \(\$ 240\)

B. \(25 \%\) chance to gain \(\$ 1,000\) and \(75 \%\) chance to gain \(\$ 0\)

b. Choose between \(\mathrm{C}\) and \(\mathrm{D}\) :

C. A sure loss of \(\$ 700\)

D. \(75 \%\) chance to lose \(\$ 1,000\) and \(25 \%\) chance to lose nothing

c. Choose between \(\mathrm{E}\) and \(\mathrm{F}\) :

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 \(\mathbf{b}\) using mathematical expectation as a basis for selecting your answers.

f. Conduct a survey of at least 10 people and summarize your results.