O Reading 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 box until you have obtained three of these prizes. (a) What is the probability that you purchase x boxes that do not have the desire urize? O nb(x; 3, 2, 10) O h(x; 3, 0.2) O nb(x; 3, 0.2) O b(x; 3, 0.2) O h(x; 3, 2, 10) O b(x; 3, 2, 10) (b) What is the probability that you purchase five boxes? (Round your answer to four decimal places.) (c) What is the probability that you purchase at most five boxes? (Round your answer to four decimal places.) (d) How many boxes without the desired prize do you expect to purchase? How many boxes do you expect to purchase?

For a fair coin tossed three times, the eight possible simple events are HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. Let X = number of tails. Find the probability distribution for X by filling in the table showing each possible value of X along with the probability that value occurs. 0 k P(X = k) 1 2 3

K Suppose there is a 22.1% probability that a randomly selected person aged 30 years or older is a smoker. In addition, there is a 24.3% probability that a randomly selected person aged 30 years or older is male, given that he or she smokes. What is the probability that a randomly selected person aged 30 years or older is male and smokes? Would it be unusual to randomly select a person aged 30 years or older who is male and smokes? The probability that a randomly selected person aged 30 years or older is male and smokes is Would it be unusual? O Yes O No www (Round to three decimal places as needed.). wew