binomial probability

Question

A company decides to implement the following policy: "If more than 1 of your calls that we review are below 80% on the quality score, then you will have to take training". If a representative has 9 calls that would earn a score above 80% and 2 that would earn a score below 80%, what is the probability that if they choose 3 calls to sample, 2 of them will earn a quality score that is below 80%.

Answer 1

Rep has 9 good calls and 2 bad calls

When you select three you could get 2 bad calls and 1 good call as follows:

 

Good Bad Bad -- probability( 9/11)*(2/10)*(1/9) = 2/110

Bad Good Bad -- probability (2/11)*(9/10)*(1/9) = 2/110

Bad Bad Good -- probability (2/11)*(1/10)*(9/9) = 2/110

 

We need to add the probabilities of these three evens to get the probability we want. That is 6/110