There are 8 candidates for a position. The candidates are interviewed independen
ID: 3023686 • Letter: T
Question
There are 8 candidates for a position. The candidates are interviewed independently by each member of a committee that has 4 people on it. A candidate will be hired if she is chosen by at least 3 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
There are 8 candidates for a position. The candidates are interviewed independently by each member of a committee that has 4 people on it. A candidate will be hired if she is chosen by at least 3 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)?
Probability of getting first rank = 1/8 =0.125
Binomial distribution used
p=0.125 n=4
P(X=x) = (nCx) px (1-p)n-x
P( X=4) = 0.0002
What is the probability that a candidate will be selected with only one dissenting vote (all but one committee members choose the same person)?
p( x=3) = 0.0068
What is the probability that a candidate will be selected?
P(selected) =P(x=3)+P(x=4) =0.0068+0.0002 =0.007
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