27 lackboard.sc.edu/bbcswebdav/pid-11793680-dt-content-rid-21316256_2/courses/MA

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27 lackboard.sc.edu/bbcswebdav/pid-11793680-dt-content-rid-21316256_2/courses/MATH1 e the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary. 25) For mutually exclusive events X1, X2, and X3, let P(X1) 0.54, PX2) 0.15, and PX3)- 0.31. Also, 25) P(YX1) = 0.40, P(YX2)-0.30, and P(YX3)-060. Find PX2'Y). B) 0.20 A) 0.42 C) 0.48 D) 0.10 the rule of total probability to find the indicated probability 26) Two shipments of components were received by a factory and stored in two se separate bins 26) Shipment I has 4% of its contents defective, while shipment ll has 3% of its contents defective. If it is equally likely an employee will go to either bin and select a component randomly, what is the probability a selected component is defective? A) 0.07 B) 0.035 C) 7 D)35 rovide an appropriate response. 27) A company manufactures shoes in three different factories. Factory Omaha Produces 25% of the 27 company's shoes, Factory Chicago produces 60%, and factory Seattle produces 15%. One percent of the shoes produced in Omaha are mislabeled, 0.5 % of the Chicago shoes are mislabeled, and 2% of the Seattle shoes are mislabeled. If you purchase one pair of shoes manufactured by this company and you determine they are mislabeled what is the probability they were made in Omaha? , A) 0.333 B) 0.353 C) 0.294 D) 0.070 Use Bayes' rule to find the indicated probability. 28) 53% of the workers at Motor works are female, while 31% of the workers at City Bank are female. 888a 8 9 4

Explanation / Answer

25) P(X2/Y)

= 0.15*0.30/(0.40*0.54+0.30*0.15+0.60*0.31)

= 0.10

26) P(defective) = 0.5*0.04+0.5*0.03 = 0.035

27) (0.25*0.01)/(0.25*0.01+0.60*0.005+0.15*0.02)

= 0.294

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