12. [1/12 Points] DETAILS PREVIOUS ANSWERS This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exprolce A market survey shows that 509% of the population used Brand X laundry detergent last year, 6% of the population gave up doing Its laundry last year, and 5%% of the population used Brand * and then gave up doing laundry last year. Are the events of using Brand * 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." Ancall 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), AX), and R(G n X) and then compare P(G n X) to P(G) - AX). Because 65% of the population gave up doing laundry, the probability that someone quit doing laundry is RG) - 0.06. Similarly, 50% of the population used Brand X, so the probability that someone was a Brand X user is RX) - 12 Furthermore, 5%% of the population used Brand * and then gave up doing laundry, so the probability that someone was Initially a Brand * user and then quit doing laundry Is P(Gn X) - 0.1 Submit Skip (you cannot come back]