Question

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

Answer 1

Probability of customer of second branch being unsatisfied is
`0.097`

Step-by-step explanation

Percent of customer registered with first branch
`= 0.7`

Percent of customer registered with second branch
`= 0.3`

Customer satisfaction at the first branch
`= 0.88`

Customer satisfaction at the second branch
`= 0.97`

Probability of customer of second branch being unsatisfied

`= (0.30 * (1-0.97))/(0.30 * (1-0.97) + 0.70 * (1-0.88)) \\= (0.30 * 0.03)/(0.30 *0.03 + 0.70 * 0.12) \\= 0.0967\\= 0.097`