Question

A large American company manufactures watches under three brand names, which we shall refer to as A, B and C. These three brands of watches are sold in Australia with a one year unconditional warranty. The watches are repaired free of charge during the warranty period at a national service centre located in Sydney. Long historical company records reveal that 50% of the company’s watches sold in Australia are brand A, 30% are brand B and 20% are brand C. In addition, for brand A the proportion of watches that need to be repaired under warranty is 30%. The corresponding proportions for the other brands are: 40% for brand B and 30% for brand C.

a) Suppose that a watch made by the American company is selected at random, what is the probability that it will be repaired under warranty?

b) If a watch needs to be repaired under warranty, what is the probability that it is brand B?

The company is thinking about instituting a policy of supplying customers with a replacement watch free of charge during the warranty period once a major fault occurs in the watch. This suggestion was the outcome of a recent study, which showed that the policy of repairing watches with major faults has not been cost effective. The company records reveal that for brand A the proportion of watches that have no major faults while under warranty is: 80%. The corresponding proportions for the other brands are: 70% for brand B and 90% for brand C.

c) Suppose that a watch made by the American company is selected at random, what is the probability that it will experience one or more major faults while under warranty?

Answer 1