The teacher was amazed by the success his students achieved in the homework assignment,and decided to reward the class by bringing homemade cupcakes. He baked 30 cupcakes, onefor each student, but the vanilla frosting was only enough for 10 of them. To make it fair, heput the cupcakes in a box and had each student pick a cupcake without knowing whether it isfrosted. You are the fifteenth student to get a cupcake.

(a) What is the probability that you will be the first to get a frosted cupcake?

(b) What is the probability that all the frosted cupcakes were taken already?

(c) Two students received frosted cupcakes so far. Your rewards from eating a non-frostedand a frosted cupcake are rn and rf respectively (rn < rf ). Your friend who is last in theline makes an offer that if you get a frosted cupcake and she doesn’t, she will pay you $2to switch cupcakes with her.

i. What is your expected reward if you don’t accept the deal?

ii. What is your expected reward if you accept the deal?

iii. For which value of rf should you accept the deal? (write an expression that dependson rn)

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