The probability that a randomly selected box of a certain type of cereal has a particular prize is .2. Suppose you purchase box after until you have obtained two of these prizes. a. What, is the probability that you purchase x boxes that do not have the desired prize? b. What is the probability that you purchase four boxes? c. What is the probability that you purchase at most four boxes? d. How many boxes without the desired prize do you expect to purchase? How many boxes do you expect to purchase?

Answer : Step 1 : Given the probability that a randomly selected box of a certain type of cereal has a particular prize is 0.2. Suppose you purchase box after until you have obtained two of these prizes. a). Now we have to find the probability that you purchase x boxes that do not have the desired prize. We purchase x boxes that do not have the desired prize is P(do not have the desired prize) =1-(0.2)x Step 2 : b). Now we have to the probability that you purchase four boxes. P(purchase four boxes) = (0.2) 4 P(purchase four boxes) = (0.2) (0.2) (0.2) (0.2) P(purchase four boxes) = 0.0016