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March 28, 2017

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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.

  • statistics - ,

    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
    =

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