Answered: Step 2 Now, use P(G) = 0.04 and P(X) =…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Transcribed Image Text:A market survey shows that 50% of the population used Brand X laundry detergent last year, 4% of the population gave up doing its laundry last year, and 5% 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? Step 1 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 n X is equal to the product of the probabilities of X and of G. That is, if and only if P(G n X) = P(G) · P(X). To answer the question, calculate P(G), P(X), and P(G n X) and then compare P(G nx) to P(G) · P(X). Because 4% of the population gave up doing laundry, the probability that someone quit doing laundry is P(G) = 0.04. Similarly, 50% of the population used Brand X, so the probability that someone was a Brand X user is P(X) = 0.50 0.50 Furthermore, 5% 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 n X) = 0.05 0.05 Step 2 Now, use P(G) = 0.04 and P(Xx) = 0.50 to calculate P(G) · P(X). Then compare that result to P(G n X) = 0.05. P(G) · P(X) = 0.04 - = Since P(G n X) ---Select--- equal to P(G) · P(X), events X and G --Select--- independent. Submit Skip (you cannot come back)

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