Use the Rule of Total Probability
-A company manufactures shoes in three different factories. Factory Omaha Produces 25% of the 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 what is the probability that the shoes are mislabeled
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.P(mislabeled) = P(Omaha) * P(mislabeled | Omaha) + P(Chicago) * P(mislabeled | Chicago) + P(Seattle) * P(mislabeled | Seattle)= 0.25 * 0.01 + 0.60 * 0.005 + 0.15 * 0.02= 0.0025 + 0.003 + 0.003= 0.009