Question

The investigation of consumer product complaints by the Federal Trade Commission (FTC) has
generated much interest by manufactures in the quality of their products. A manufacturer of an
electromechanical kitchen utensil conducted an analysis of a large number of consumer
complaints and found that they fell into the six categories shown in Table 3.6. If a consumer
complaint is received, what is the probability that the cause of the complaint was product
appearance given that the complaint originated during the guarantee period?
Distribution of product complaints
Reason for Complaint
Complaint Origin Electrical Mechanical Appearance Totals
During guarantee period 18% 13% 32% 63%
After guarantee period 12% 22% 3% 37%
Totals 30% 35% 35% 100%

Answer 1

If a consumer complaint is received, what is the probability that the cause of the complaint was product appearance given that the complaint originated during the guarantee period? 

Formula:

P(A/B)= $\frac{P(A and B)}{P(B)}$

Solution :

P(the cause of the complaint was product appearance/the complaint originated during the guarantee period)= $\frac{P(appearance)}{P(During -guarantee -period)}$

=$\frac{0.32}{0.63}$

=0.5079 or 50.79%