SOLUTION: 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 B

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(52802) (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 (!)

RELATED QUESTIONS
Nine customers at a supermarket are asked if they use brand X laundry soap. In general,... (answered by scott8148)

Nine customers at a supermarket are asked independently if they use brand X laundry soap. (answered by stanbon)

A previous survey shows that some 60% of customers prefer brand X. A sample survey is... (answered by stanbon)

Shelly is shopping for laundry detergent,mustard,and canned tuna.She is trying to decide... (answered by Theo)

A survey of 30 adults found that the mean age of a person�s primary vehicle is 5.6 years. (answered by stanbon)

The mean preparation fee H&R Block charged retail customers last year was $183 (the Wall... (answered by Theo)

For each load of laundry.Sandy uses either a quarter of a bottle or half of a bottle of... (answered by macston)

Survey Results A company is taking a survey to find out whether people like its product. (answered by edjones)

A city has a population of 330000 people. Suppose that each year the population grows by... (answered by greenestamps)