Question

A market research company requires each of its field workers to conduct 10 interviews per day. Not everybody approached by a field worker agrees to participate in an interview. In fact, only 60% of approaches lead to an interview. Assuming a Negative Binomial distribution, what is the probability that the 10th interview is obtained from the 15th person approached?

Answer 1

if X follows a negative binomial distribution with parameters r and p

then, probability that the success occurs in the trial is :

here, X follows Negative binomial with parameters r=10, and p = 0.60

so,

or,

so, P(X=15) = 0.1240

so, answer = 0.1240