Posted by James on .
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 Bayesâ€™ theorem to find the probability that a complaint was from a customer whose service was provided by their own employees.

statistics 
MathMate,
E=calls by employees
C=complaints
P(E)=10.30=0.70
P(CE')=0.15
P(CE)=0.05
P(C)=0.7*0.05+0.3*0.15=0.08
P(EC)=P(E∩C)/P(C)
=P(C∩E)/P(C)
=P(CE)*P(E)/P(C) (Bayes' theorem)
=0.05*0.7/0.08
=35/80
=7/16
=