Mathematics, 21.09.2019 01:20, Yoma321
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.
Answers: 2
![P(C=1|T=1)=q(\sum_{i=15}^{20}\binom{20}{i} p^i(1-p)^{20-i})( \sum_{i=15}^{20}\binom{20}{i}[qp^i(1-p)^{20-i} + (1-q)p^{20-i}(1-p)^i])^{-1}](/tpl/images/0248/0235/fde72.png)
![P(T=1)=q\sum_{i=15}^{20}f_1(i) + (1-q)\sum_{i=15}^{20}f_0(i)\\P(T=1)=\sum_{i=15}^{20}\binom{20}{i}[qp^i(1-p)^{20-i} + (1-q)p^{20-i}(1-p)^i)]](/tpl/images/0248/0235/4052e.png)
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Acompany is interviewing potential employees. suppose that each candidate is either qualified, or un...
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