In the mid-1990s, Colgate-Palmolivedeveloped a new toothpaste for the U.S. market, Colgate Total, withan antibacterial ingredient that was already being successfullysold overseas. At that time, the word antibacterial was not allowedfor such products by the Food and Drug Administration (FDA). Inresponse, the name “Total” was given to the product in the UnitedStates. The one word would convey that the toothpaste is the“total” package of various benefits. Young & Rubicam developedseveral commercials illustrating Total’s benefits and tested thecommercials with focus groups. One commercial touting Total’slong-lasting benefits was particularly successful. The product waslaunched in the United States in January of 1998 using commercialsthat were designed from the more successful ideas of the focusgroup tests. Suppose 32% of all people in the United States saw theTotal commercials. Of those who saw the commercials, 40% purchasedTotal at least once in the first 10 months of its introduction.According to U.S. Census Bureau data, approximately 20% of allAmericans were in the 45-64 age category. Suppose 24% of theconsumers who purchased Total for the first time during the initial10-month period were in the 45-64 age category. Within three monthsof the Total launch, Colgate-Palmolive grabbed the number onemarket share for toothpaste. Ten months later, 21% of all U.S.households had purchased Total for the first time. The commercialsand the new product were considered a success. During the first 10months of its introduction, 43% of those who initially tried Totalpurchased it again.   

1. What percentage of U.S. households purchased Total at leasttwice in the first 10 months of its release?

1. Can you conclude the initial purchase of Total was independentof age? Use a quantitative argument to justify your answer.

1. Calculate the probability that a randomly selected U.S.consumer is either in the 45-64 age category or purchased Totalduring the initial 10-month period.

1. What is the probability that a randomly selected personpurchased Total in the first 10 months given that the person is inthe 45-64 age category?

e. What percentage of people who did not see the commercialspurchased Total at least once in the first 10 months of itsintroduction?