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 and you determine they are mislabeled whatis the probability they were made in Omaha?
A) 0.294
B) 0.353
C) 0.333
D) 0.070

Question

Quizplus · Accepted Answer

0.294To find the probability that a mislabeled shoe came from Omaha, we use Bayes' theorem. First, calculate the overall probability of getting a mislabeled shoe:- Omaha: $0.25 \times 0.01 = 0.0025$- Chicago: $0.60 \times 0.005 = 0.003$- Seattle: $0.15 \times 0.02 = 0.003$Total probability of a mislabeled shoe: $0.0025 + 0.003 + 0.003 = 0.0085$.Then, the probability that a mislabeled shoe came from Omaha is the proportion of Omaha's contribution to the total mislabeled shoes:$\frac{0.0025}{0.0085} \approx 0.294$.

A Company Manufactures Shoes in Three Different Factories