In the mid-1990s, Colgate-Palmolive developed a new toothpaste for the U.S. market, Colgate Total, with an antibacterial ingredient that was already being successfully sold overseas. However, the word antibacterial was not allowed for such products by the Food and Drug Administration rules. So Colgate Palmolive had to come up with another way of marketing this and other features of their new toothpaste to U.S. consumers. Market researchers told Colgate-Palmolive that consumers were weary of trying to discern among the different advantages of various toothpaste brands and wanted simplification in their shopping lives. In response, the name "Total" was given to the product in the United States: The one word would convey that the toothpaste is the "total" package of various benefits.

Discussion

1. What probabilities are given in this case? Use these probabilities and the probability laws to determine what percentage of U.S. households purchased Total at least twice in the first 10 months of its release.

2. Is age category independent of willingness to try new products? According to the U.S. Census Bureau, approximately 20% of all Americans are in the 45-64 age category. Suppose 24% of the consumers who purchased Total for the first time during the initial 10-month period were in the 45-64 age category. Use this information to determine whether age is independent of the initial purchase of Total during the introductory time period. Explain your answer.

3. Using the probabilities given in Question 2, calculate the probability that a randomly selected U.S. consumer is either in the 45-64 age category or purchased Total during the initial 10-month period. What is the probability that a randomly selected person purchased Total in the first 10 months given that the person is in the 45-64 age category?

4. Suppose 32% of all toothpaste consumers in the United States saw the Total commercials. Of those who saw the commercials, 40% purchased Total at least once in the first 10 months of its introduction. Of those who did not see the commercials, 12.06% purchased Total at least once in the first 10 months of its introduction. Suppose a toothpaste consumer is randomly selected and it is learned that they purchased Total during the first 10 months of its introduction. Revise the probability that this person saw the Total commercials and the probability that the person did not see the Total commercials.