Acompany is interviewing potential employees. suppose that each candidate is either qualified, or unqualified with given probabilities q and 1 − q, respectively. the company tries to determine a candidate’s qualifications by asking 20 true-false questions. a qualified candidate has probability p of answering a question correctly, while an unqualified candidate has a probability p of answering incorrectly. the answers to different questions are assumed to be independent. if the company considers anyone with at least 15 correct answers qualified, and everyone else unqualified, give a formula for the probability that the 20 questions will correctly identify someone to be qualified or unqualified.