The call center of an internet provider company processes both technical help ca

Question

The call center of an internet provider company processes both technical help calls and sales calls. Equal numbers of technical and sales calls arrive every day on average. Fifty percent of technical calls are completed in less than two minutes, while the remaining fifty percent take more than two minutes. Ninety five percent of sales calls are completed in less than two minutes, while the remaining five percent call are completed in more than two minutes. An operator tells you that he just processed a phone call in more than two minutes without telling you if it was a sales or a technical call. Given that the phone call took more than two minutes what is the probability of being a technical help call?

Explanation / Answer

Let the total number of calls handles be 100. Then we can make a table as below ...

Given that the phone call took more than two minutes the probability of it being a technical help call

= 25/30 = 5/6 = 0.8333

< 2minutes 2 minutes Total Technical 50% of 50 = 25 50 - 25 = 25 50 Sales 90% of 50 = 45 50 - 45 = 5 50 Total 70 30 100

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