A company is interviewing potential employees Suppose that e

A company is interviewing potential employees. Suppose that each candidate is either quali?ed, or unquali?ed with given probabilities q and 1 ? q, respectively. The company tries to determine a candidate

Solution

If the company considers anyone with at least 15 correct answers quali?ed

probability that candidate is qualified = 20C15*q^15(1-q)^5 + 20C16q^16(1-q)^4 + 20C17q^17(1-q)^3 +   20C18q^18(1-q)^2   + 20C19*q^19(1-q) + 20C20*q^20

probability that candidate is not qualified = 1- (20C15*q^15(1-q)^5 + 20C16q^16(1-q)^4 + 20C17q^17(1-q)^3 +   20C18q^18(1-q)^2   + 20C19*q^19(1-q) + 20C20*q^20)

formula for the probability that the 20 questions will correctly identify someone to be quali?ed or unquali?ed = P1/P2