Question

Problem 8.
A company that manufactures shoes has three factories. Factory 1 produces 25% of the
company's shoes, Factory 2 produces 60%, and Factory 3 produces 15%. One percent of the
shoes produced by Factory 1 are mislabeled, 0.5% of those produced by Factory 2 are
mislabeled, and 2% of those produced by Factory 3 are mislabeled. If you purchase one pair of
shoes manufactured by this company, what is the probability that the shoes are mislabeled?

Answer 1

Given data:

Factory	1	2	3
Production %	25%	60%	15%
Mislabeled	1%	0.50%	2%

Factory	1	2	3
Production % ,   (P1)	25%	60%	15%
Mislabeled %,    (P2)	1%	0.50%	2%
Mislabeled probability, (P)	0.25%	0.30%	0.30%

P = P1 * P2

probability that the shoes are mislabeled = sum of P

probability that the shoes are mislabeled = 0.25 +0.3 +0.3= 0.85%

probability that the shoes are mislabeled is 0.85%