P22. a.Suppose that you are in class and your instructor makes you the following legitimate offer. Take out a piece of paper and without communicating with your classmates, write one of the following messages under your name:

I share the wealth and will receive $1,000 if everyone in the class checks this box. I will not share the wealth and want a certain $100. If everyone checks the first box, then all will receive $1,000. If at least one person checks the second box, then only those who check the second box will receive $100. Which box would you check, and why?
b.Repeat, except change the stakes to $110 and $100, respectively.
c. Repeat, except change the stakes to $10,000 and $10, respectively.
d. Repeat, except change the stakes to be an A grade in the class if everyone checks the first box, but if anyone checks the second box, the following will occur: Those who check it will have a 50% chance of an A and a 50% chance of a F, but those who do not check the second box will be given an F in this course.
P23. The Game of WIN. Construct a set of nonstandard dice as shown here.
INSERT ILLUSTRATION 09.054 HERE
Suppose that your opponent picks die A and that you pick die B. Then we can enumerate the sample space as shown here.
INSERT ILLUSTRATION 09.055 HERE
INSERT ILLUSTRATION 09.055 TABLE HERE
We see that the probability of A winning is 24/36, or 2/3. If you were to play the game of WIN, would you choose your die first or second?