Determining the probability from the given Colgate story.

Colgate-Palmolive Makes a "Total" Effort

In the mid-1990s, Colgate-Palmolive had 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.

Young & Rubicam developed several commercials illustrating Total's benefits and tested the commercials with focus groups. One commercial touting Total's long-lasting benefits were particularly successful. Meanwhile, in 1997, Colgate-Palmolive received FDA approval for Total, five years after the company had applied for it.

The product was launched in the United States in January of 1998 using commercials that were designed from the more successful ideas of the focus group tests. A print campaign followed.

Within three months, Colgate-Palmolive grabbed the number one market share for toothpaste. Ten months later, 21% of all U.S. households had purchased Total for the first time. During the same time period, 43% of those who initially tried Total purchased it again. Colgate Total had been successfully introduced into the U.S. market.

1) What probabilities are given in this case? Use these probabilities and the probability law to determine what percentage of the U.S. households

purchased Total at least twice in the first 10 months of its release.

Hint: Apply a Law of Multiplication here.

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...ives us the following probabilities:
<br>P(A) = 0.21
<br>P(B|A) = 0.43
<br>We are supposed to find the probability that ...