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) =

Name: A market survey shows that 30% of the population used Brand X laundry
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Description: 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 usi

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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)

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) =

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