A company manufactures shoes in three different factories. Factory Omaha Produces 25% of the companyʹsshoes, Factory Chicago produces 60%, and factory Seattle produces 15%. One percent of the shoes produced inOmaha 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 what is the probability that the shoes aremislabeled? Round to the nearest thousandth.
A) 0.009
B) 0.036
C) 0.043
D) 0.020

Question

Quizplus · Accepted Answer

The probability of a shoe being mislabeled is the sum of the probabilities of the shoe being produced in each factory and mislabeled. The probability of a shoe being produced in Omaha and mislabeled is 0.25 * 0.01 = 0.0025. The probability of a shoe being produced in Chicago and mislabeled is 0.60 * 0.005 = 0.003. The probability of a shoe being produced in Seattle and mislabeled is 0.15 * 0.02 = 0.003. The total probability of a shoe being mislabeled is 0.0025 + 0.003 + 0.003 = 0.0085, which rounds to 0.009.

A Company Manufactures Shoes in Three Different Factories