A company is interviewing potential employees. Suppose that each candidate is either qualified, or unqualified with given probabilities 0.62 and 0.38, respectively. The company tries to determine a candidate's qualifications by asking 20 true-false questions. A qualified candidate has probability 0.79 of answering a question correctly, while an unqualified candidate has a probability 0.79 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 the probability that the 20 questions will correctly identify someone to be qualified or unqualified.

If X is the random variable 'number of correctly answered questions by a qualified candidate' then X ~ Binomial(n = 20, p = 0.79) and you need to calculate Pr(X > 14).

If Y is the random variable 'number of correctly answered questions by a non-qualified candidate' then Y ~ Binomial(n = 20, p = 0.21) and you need to calculate Pr(Y < 15).

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