Question

Use the Bayes’ formula to answer the following: A ceramics company has two production facilities, one in Ladysmith and one in Duncan. The same type of bowl is made at both factories. The Ladysmith factory produces 25% of the company’s bowls and the Duncan factory produces the remaining bowls. All bowls produced from the two factories are sent to a central facility for sale. After extensive sampling, the quality assurance manager has determined that 17% of the bowls produced in Ladysmith and 29% of the bowls produced in Duncan are unusable due to poor quality.

(i) What is the probability of poor quality?

(ii) What is the probability of good quality?

(iii) What is the probability that a bowl was produced at the Ladysmith factory, given that it is of poor quality?

(iv) What is the probability that a bowl was produced at the Duncan factory, given that it is of good quality?

Answer 1