There are three candidates for a position. The candidates are interviewed indepe

Question

There are three candidates for a position. The candidates are interviewed independently by each member of a three person committee. A candidate will be hired if she is ranked first by at least two members of the committee. If the committee members cannot really distinguish among the candidates and just rank them at random, what is the probability that a candidate will be selected?

The wording of this one is kind of strange, so let's answer both, a particular candidate will get the job, and one of the three will get the job. Really need to see the setup.

Explanation / Answer

both the questions you state are the same question. because the question does not state that one particular candidate is more likely to be selected than any other we can assume that all three are equally likely. I believe the question is actually asking. IF it comes down all three members randomly ranking a candidate, what is the probability that the candidate will then be selected. In order for a candidate to be selected, two of the three committee persons need to rank him or her first. lets call these people A,B,&C and we want the Probability that A will win. The probability that any given committee person ranks candidate A first is: =(number of orderings in which A is first)/(total number of orderings) =({A,B,C},{A,C,B})/({A,B,C},{A,C,B},{B,A,C},{B,C,A},{C,B,A},{C,A,B}) =2/6=1/3 This is the probability that just one committee person ranks them first. The probability that they win is: =P(2 select A)+P(all 3 select A) =((3 choose 2)*(1/3)^2*(2/3))+(1/3)^3 where "3 choose 2" is the number of ways that two of the three committee members could select A.

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