There are 4| candidates for a position. The candidates are interviewed independe

Question

There are 4| candidates for a position. The candidates are interviewed independently by each member of a committee that has 41 people on it. A candidate will be hired if she is chosen by at least 31 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

a) Probability that a candidate will be selected with unanimous vote

P= 1/((4C3)*(4C1)

P=1/(4*4)

P=1/16

b)  Probability that a candidate will be selected with only one dissenting vote

P=4C3/(4C3*4C1)

P=4/16=1/4

c)  Probability that a candidate will be selected

P=1/4

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