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A distributor has two branches in TX. First branch has 70% of the customers, and the second one has the remaining 30%. The customer satisfaction at the first branch is 88% and at the second branch is 97%. The distributor has a centralized call center serving both branches. If an unsatisfied customer makes a call to the call center. What is the probability that it is a customer of the second branch

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Answer

Probability of customer of second branch being unsatisfied is [tex]0.097[/tex]

Explanation

Percent of customer registered with first branch [tex]= 0.7[/tex]

Percent of customer registered with second branch [tex]= 0.3[/tex]

Customer satisfaction at the first branch [tex]= 0.88[/tex]

Customer satisfaction at the second branch [tex]= 0.97[/tex]

Probability of customer of second branch being unsatisfied

[tex]= \frac{0.30 * (1-0.97)}{0.30 * (1-0.97) + 0.70 * (1-0.88)} \\= \frac{0.30 * 0.03}{0.30 *0.03 + 0.70 * 0.12} \\= 0.0967\\= 0.097[/tex]

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