Jayne is playing a simple game with a fair 20-sided object. There are 9 blue sides, 9 red sides, 1 green side, and 1 black side. If the object lands with a blue side up, Jayne will win 5 points; if it lands with a red side up, she'll lose 10 points. Similarly, if it lands with the green side up, she will win 30 points, and if the black side is facing up, then she will lose 20 points. Based on this information, answer the following questions:

(A) What is the probability that the chance cube will land with a blue face up on any given turn?

(B) What is the expected value of each roll of the object?

(C) Suppose it costs Jayne 1 point each time she rolls the cube. How much

does this change the expected value?

(D) Suppose Jayne is risk averse, with an initial wealth of 400 points and a

utility function of Wealth. Should she continue to play the game, or

should she cash in her points for toys (a no-risk proposition)?

(E) Zoe is more adventurous than Jayne. Zoe has a utility function U = W2, where W = Wealth. If her initial wealth is 500 points, should she play

the game?