A firm has 30% of its service calls made by a contractor, and 15% of these calls result in customer complaints. The other 70% of the service calls are made by their own employees, and these calls have a 5% complaint rate. Use Bayes’ theorem to find the probability that a complaint was from a customer whose service was provided by their own employees.

Answer 1

E=calls by employees
C=complaints

P(E)=1-0.30=0.70
P(C|E')=0.15
P(C|E)=0.05
P(C)=0.7*0.05+0.3*0.15=0.08
P(E|C)=P(E∩C)/P(C)
=P(C∩E)/P(C)
=P(C|E)*P(E)/P(C) (Bayes' theorem)
=0.05*0.7/0.08
=35/80
=7/16
=