Question

A recruiting firm finds that 20% of the applicants for a particular sales position are fluent in both English and Spanish. Suppose that four jobs requiring fluency in English and Spanish are open. Find the probability that two unqualified applicants are interviewed before finding the fourth qualified applicant if the applicants are interviewed sequentially.

Answer: Negative Binomial 0.01 (I need help with how you get to the answer)

Answer 1

Let X denotes the number of unqualified applicants are interviewed before finding the fourth qualified applicant.

X ~ Negative Binomial( r = 4, p = 0.2)

The probability mass function of X is

Now,

The probability that two unqualified applicants are interviewed before finding the fourth qualified applicant