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 it was labeledcorrectly?
A) 0.991
B) 0.035
C) 0.9
D) 0.08

Question

Quizplus · Accepted Answer

To calculate the probability that a pair of shoes is labeled correctly, we need to consider the production and mislabel rates for each factory, then subtract the mislabel rates from 1 to find the correct label rates. For Omaha: $0.25 \times (1 - 0.01) = 0.25 \times 0.99$, for Chicago: $0.60 \times (1 - 0.005) = 0.60 \times 0.995$, and for Seattle: $0.15 \times (1 - 0.02) = 0.15 \times 0.98$. Adding these probabilities gives the overall probability of a shoe being labeled correctly: $0.25 \times 0.99 + 0.60 \times 0.995 + 0.15 \times 0.98 = 0.991$.

A Company Manufactures Shoes in Three Different Factories