First, we need to test whether the two events are independent. Use X to denote the event described by "A person used Brand X,"

Question

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 gave
up doing laundry."
Recall that the two events are independent if and only if the probability of GnX is equal to the product of the
probabilities 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 is
P(G) = 0.06.
Similarly, 70% of the population used Brand X, so the probability that someone was a Brand X user is
P(X) =
Furthermore, 7% of the population used Brand X and then gave up doing laundry, so the probability that
someone was initially a Brand X user and then quit doing laundry is P(Gnx) =

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