If they are qualified and have a nomination, the chances are a over 50% that they will be offered an appointment. Now, that is purely rough odds and does not account for the strength of their application. Obviously, if you are min performing on one or more categories, your chances are less than someone who boasts strong academics, test scores, athletics, leadership activities, and did well in interviews and essay writing!
Here is the admissions breakdown for the class of 2017
Applicants 9,706
Candidate Pool 6,967
Qualified Candidates 2,277
Offers of Admission 1,475
Total Admitted 1,190