(1 point) You need at least nine decimal places on this problem. You may want to
ID: 3354535 • Letter: #
Question
(1 point) You need at least nine decimal places on this problem. You may want to use fractions instead There are 6 candidates for a position. The candidates are interviewed independently by each member of a committee that has 6 people on it. A candidate will be hired if she is chosen by at least 5 members of the committee. In reality, the committee members cannot really distinguish among the candidates and just choose at random with no biases What is the probability that a candidate will be selected with a unanimous vote (all committee members choose the same person)? What is the probability that a candidate will be selected with only one dissenting vote (all but one committee members choose the same person)? What is the probability that a candidate will be selected?Explanation / Answer
P(a candidate will be selected with a unanimous vote) = [P(a member chosing a candidate)]6
= (1/6)6
= 1/46656
P(a candidate will be selected with only one dissenting vote) = 6C1 x (5/6) x (1/6)5
= 5/7776
P(a candidate will be selected) = (1/46656) + (5/7776)
= 31/46656
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