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First, we need to test whether the two events are independent.Use X to denote the...

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Basic Math

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First, we need to test whether the two events are independent.Use X to denote the event described by "A person used Brand X," and G to describe the event "A person gaveup doing laundry."Recall that the two events are independent if and only if the probability of GnX is equal to the product of theprobabilities of X and of G. That is, if and only if P(GMX) = P(G)- P(X).To answer the question, calculate P(G), P(X), and P(GNX) and then compare P(GNX) to P(G)- P(X).Because 6% of the population gave up doing laundry, the probability that someone quit doing laundry isP(G) = 0.06.Similarly, 70% of the population used Brand X, so the probability that someone was a Brand X user isP(X) =Furthermore, 7% of the population used Brand X and then gave up doing laundry, so the probability thatsomeone was initially a Brand X user and then quit doing laundry is P(Gnx) =

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