There are n applicants for the director of computing. The applicants are interviewed independently by each member of the three-person search committee and ranked from 1 to n. A candidate will be hired if he or she is ranked first by at least two of the three interviewers. Find the probability that a candidate will be accepted if the members of the committee really have no ability at all to judge the candidates and just rank the candidates randomly. In particular, compare this probability for the case of three candidates and the case of ten candidates.
Probability of getting first rank = 1/n
The candidate will be accepted if two or three of the judges rank him as first
= Prob (two judges rank him first) + Prob (three judges rank him first)
= 3C2*(1/n)^2 + 3C3*(1/n)^3
A slight disagreement with you.
In the question stem word atleast TWO is used.
So the required probability = (probability of any two member will give the candidate 1st rank) * (probability that the third member does not give 1st rank to the candidate) + probability that all the members give 1st rank to the candidate
= 3C2*(1/n)^2* (1-1/n) + 3C3*(1/n)^3 = (3n-2)/n^3
Do you agree?