Suppose Jasmine is invited to the following dice gamble: a fair die with 6 sides showing a different number from 1 to 6 will be cast. The number on the top side of the die will be the prize money to the player. She needs to pay $4 to enter the gamble. Answer the following questions.
a) Calculate the expected value of the gamble. Is this a fair gamble?
b) If Jasmine is a risk-neutral person, would she enter the gamble?
c) Suppose Jasmine can pay $7 instead of $4 to double her reward. For example, a cast with 6 would earn her $12. Is she going to enter the gamble?