exercise:Caef148c3b: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> There are <math>n</math> 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 <math>n</math>. A candidate will be hired if he or she is ra...") |
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There are <math>n</math> 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 <math>n</math>. A candidate will be hired if he or she is ranked | |||
applicants are interviewed independently by each member of the three-person search | |||
committee and ranked from 1 to <math>n</math>. 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 | 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 | candidate will be accepted if the members of the committee really have no ability at | ||
Latest revision as of 22:43, 12 June 2024
There are [math]n[/math] 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 [math]n[/math]. 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.