Refer to Exercise 10. The company has two positions open. They will interview candidates until two qualified candidates are found. Let \(Y\) be the number of candidates interviewed up to and including the second qualified candidate.

a. What is the smallest possible value for \(Y\) ?

b. What is the probability that \(Y\) takes on that value?

c. Let \(X\) represent the number of applicants who are interviewed up to and including the first qualified candidate. Find \(P(Y=4 \mid X=1)\).

d. Find \(P(Y=4 \mid X=2)\).

e. Find \(P(Y=4)\).

Data From Exercise 10:

Candidates for a job are interviewed one by one until a qualified candidate is found. Thirty percent of the candidates are qualified.