Tutorial Exercise 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 N X) 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) = 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) =

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.8: Probabilities Of Disjoint And Overlapping Events

Problem 2C

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Transcribed Image Text:Tutorial Exercise 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 N X) 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) = 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(Gn X) =

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