1.The probability of a randomly selected box of certain type of cereal has a particular prize is 0.15.Suppose you purchase box after box until you have obtained three of these prizes.

a.What is the expected value of the number of boxes until three have prizes, that is the expected value of the total number of boxes (total number of boxes = the number of boxes without prizes plus the number of boxes with prizes)?

b.What is the probability you purchase 4 boxes that do not contain the prize until 3 boxes have a prize?

c.What is the probability you have to purchase at most 4 boxes that do not contain the prize until 3 boxes have the prize?