Question 1179546: A market survey shows that 30% of the population used Brand X laundry detergent last year, 8% of the population gave up doing its laundry last year, and 3% of the population used Brand X and then gave up doing laundry last year. Are the events of using Brand X and giving up doing laundry independent? Is a user of Brand X detergent more or less likely to give up doing laundry than a randomly chosen person?
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
G ∩ X
is equal to the product of the probabilities of X and of G. That is, if and only if
P(G ∩ X) = P(G) · P(X).
To answer the question, calculate P(G), P(X), and
P(G ∩ X)
and then compare
P(G ∩ X)
to
P(G) · P(X).
Because 8% of the population gave up doing laundry, the probability that someone quit doing laundry is
P(G) = 0.08.
Similarly, 30% of the population used Brand X, so the probability that someone was a Brand X user is
P(X) = 0.3
Furthermore, 3% 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(G ∩ X) =
Answer by ikleyn(52800)   (Show Source):
You can put this solution on YOUR website! .
See a TWIN problem solved under this link
https://www.slader.com/discussion/question/a-market-survey-shows-that-40-of-the-populationused-brand-x-laundry-detergent-last-year-5-of-the-population-gave-up-doing-its-laundry-last-y-e9c21f04/
Consider it as your TEMPLATE.
Read it attentively.
Having this template in front of you, solve the current problem in the same way, using the same logic.
Be happy and E N J O Y (!)
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