3. A company manufactures shoes in three different factories. Factory Omaha Prod

Question

3. A company manufactures shoes in three different factories. Factory Omaha Produces 35% of the company's shoes, Factory Chicago produces 50%, and the factory in Seattle produces 15%. 3% of the shoes produced in Omaha are mislabeled, 2% of the Chicago shoes are mislabeled, and 1% of the Seattle shoes are mislabeled. a) If you purchase one pair od shoes manufactured by this company what is the probablility that the shoes are mislabeled? B) If you purchase one pair of shoes manufactured by this company and you determine they are mislabeled, What is the probablity they were made in Chicago? C) If you purchase one pair of shoes manufactured by this company, what is the probability that it was labeled correctly?

4. In a carnival game, a person wagers $2 on the roll of two dice. If the total of the two dice is 2,3,4,5 or 6 then the person gets $4 (wins$2). If the total of teh two dice is 8,9,10,11 or 12 then the person gets nothing (loses $2). If the total of the two dice is 7, the person gets $0.75 back and (loses $1.25). What is the expected value of playing the game once?

Explanation / Answer

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P[omaha & mislabelled] = 3% of 35% = 0.0105
P[chicago & mislabelled] = 2% of 50% = 0.01
P[seattle & mislabelled] = 1% of 15% = 0.0015

A. P[mislabelled] = 0.0015 + 0.01 + 0.0105 = 0.022

b) P[chicago|mislabelled] = 0.01/0.022 = 0.455

c) P(correctly) = 1 - 0.022

P = 0.978

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